These verses speak about the hypocrites who resided in Madinah, in the life-time of Prophet Muhammed (p). These people would outwardly look like they’re part of the Muslim community. But in reality they were the real enemies who wanted to destroy Islam and the Muslims. And would do anything in their path to side with enemies to harm the Muslims, 1400 years ago.
It is said that these verses were either revealed during the Banu Mustaliq campaign or just after, returning from it (Mawdudi). 
For more information on the Banu Mustaliq incident, please click on the following article: “The Banu Mustaliq Incident”
63:1 When the hypocrites come to you, [O Muhammad], they say, “We testify that you are the Messenger of God.” And God knows that you are His Messenger, and God testifies that the hypocrites are liars.
63:2 They have taken their oaths as a cover, so they averted [people] from the way of God. Indeed, it was evil that they were doing.
63:3 That is because they believed, and then they disbelieved; so their hearts were sealed over, and they do not understand.
63:4 And when you see them, their forms please you, and if they speak, you listen to their speech. [They are] as if they were pieces of wood propped up – they think that every shout is against them. They are the enemy, so beware of them. May God destroy them; how are they deluded?
Malik Ghulam Farid:
“3050. The hypocrites seem to have lost all reason and understanding since they labour under the misconception that by their wiles and glib talk they cane deceive Allah and His Prophet.
3051. A hypocrite lacks self-reliance. He is always in search of someone upon whom to lean. Or, the verse may signify that his interior does not correspond to his exterior. He so conducts himself that whole outwardly he appears to be a reasonable, dignified and honest person, inwardly he is quite hollow and rotten to the core. He seeks to please people with his glib talk but, being a coward, he suspects and sees danger everywhere.” 
Maulana Muhammad Ali:
“3a. Note how the sealing of hearts is described here. It is man’s own action which is the cause, while the sealing is but the necessary consequence.
4a. By the cry is here meant the hostile incursion of the enemy by which the tribes are surprised (LL). Whenever there was an incursion of the enemy, the hypocrites showed cowardice and thought that the Muslims would be crushed by their adversaries.” 
Dr. Muhammad Asad:
“4 Lit., “thou dost give ear to them”: i.e., hypocrisy has usually a plausible outward aspect inasmuch as it is meant to deceive.
5 Regarding my interpolation of the phrase “They deserve the imprecation”,see note 45 on the identical sentence at the end of 9:30. NOTE: 45
45 My interpolation, between brackets, of the words “they deserve the imprecation” is based on Zamakhshari’s and Razi’s convincing interpretation of this phrase. Originally, the Arabs used the expression “may God destroy him” in the sense of a direct imprecation; but already in pre-Qur’anic
Arabic it had assumed the character of an idiomatic device meant to circumscribe anything that is extremely strange or horrifying: and, according to many philologists, “this, rather than its literal meaning, is the purport [of this phrase] here” (Manor X, 399).” 
Sayyid Abul Ala Maududi:
“5 Hadrat ‘Abdullah bin ‘Abbas has stated that ‘Abdullah bin Ubayy was a strongly built, healthy, handsome and smooth-tongued person, and the same was the case with most of his companions. They were all the nobles of Madinah. When they came to sit in the Holy Prophet’s assembly, they would sit reclining on cushions against the walls and would talk agreeably and convincingly. From their outward appearance and manner of speech no one could imagine that those honourable people of the city would be so wretched and degraded in their character.
6 That is, “Those who sit reclining on cushions against the walls, are not but pieces of timber. Comparing them to timber is meant to imply that they are devoid of the moral sense which is the essence of humanity Then by comparing them to blocks of timber propped up against the wall, it has also been pointed out that they are absolutely worthless, for the timber would be useful only when it has been utilized in making of a ceiling, or a door frame, or a piece of furniture. A block of timber that has just been placed against a wall serves no useful purpose at all.”
7 This brief sentence portrays the state of their guilty conscience. Since they fully well knew what game of hypocrisy they were playing tinder the screen of their superficial faith, they always remained in a state of alarm, thinking as to when the secret of their treason might be exposed, or the believers might feel disgusted with their evil deeds and machinations and take them co task for them. If ever a cry was raised anywhere in the city, or a noise was heard; they immediately grew alarmed and thought it was directed against themselves.
8 In other words, these hidden enemies are more dangerous than the open enemies.
9 That is, “Do not be deceived by their outward appearances. Beware of them, for they can deceive you at any moment. “
10 This is not a curse but a declaration of the verdict about them by Allah that they have become worthy of His punishment and He will certainly inflict His punishment on them. It is also possible that Allah may not have used these words in their literal sense but in the meaning of a curse and condemnation according to Arabic idiom.
11 It has not been pointed out as to who perverts them from belief to hypocrisy. This by itself makes it clear that there is not one but many factors responsible for their perversion. There is Satan, there are their evil friends, and there are their own selfish motives. Someone’s wife or children become his motive, and someone is driven to perversion by the evil ones in his society, or by jealousy, spite and pride.” (Sayyid Abul Ala Maududi – Tafhim al-Qur’an – The Meaning of the Qur’an – Online source)
Tanwir al-Miqbas min Tafsir Ibn Abbas:
“(And when thou) O Muhammad (seest them) i.e. ‘Abdullah Ibn Ubayy and his two friends (their figures please thee) their bodies and appearance please you; (and if they speak) saying: we know you are Allah’s Messenger (thou givest ear unto their speech) you believe what they say and think they are truthful while they are not. ((They are)) i.e. their bodies are (as though they were blocks of wood in striped cloaks) aligned against the wall; He says: there is no goodness or light in their hearts just as dry wood has no life or moistness in it. (They deem every shout) every noise in Medina (to be against them) because of their cowardice. (They are the enemy, so beware of them) and never feel safe from them. (Allah confound them) Allah cursed them! (How they are perverted!) How they lie; it is also said this means: how they turn people away through lies!” (Tanwir al-Miqbas min Tafsir Ibn Abbas on Surah 63:4 – Online source)
In the Shade of the Qur’an By Sayyid Qutb:
“The Surah draws a unique picture of such people inviting ridicule and describing them as aimless, leading a futile existence, and nursing grudges. It presents an image of them that serves as an object of ridicule:… Thus, they are merely an outward appearance, not real human beings who respond and interact. They may look pleasant to the eye as long as they remain silent, but when they speak they show themselves to be devoid of sense and feeling. They are like timbers, but not just any kind of wood: they are propped up against a wall, unable to move.
This stone-cold picture shows the reaction of their souls, that is if they have souls at all. This is then complemented with a state of constant apprehension, perpetual dear and uncertainty:
‘They think that ever shout is directed against them.’ (Verse 4)
They know themselves to be hypocrites, covered by a thin veil of pretence, false oaths and attampts to appease. Hence, they live under the constant dread that their reality will be exposed. The Surah shows them always turning around, dreading every move and every shout. They imagine that every cry is setting a chase after them. Thus, spiritually, they are like propped up pieces of wood, but when it is a question of fear for one’s life or property, they look like a trembling reed in a storm. In both cases, they are the main enemy of the Prophet and the Muslim community:
‘They are the real enemy; so beware of them.’
They are the enemy within, hiding within Muslim ranks. Hence, they represent a greater danger than the external enemy. Therefore, the Prophet is instructed to beware of them. He is NOT, however, instructed here to kill them. Instead, he was to pursue a different course of action, one that reflected much wisdom and confidence that their schemes would come to nothing.
‘May God destroy them! How perverse they are!’ (Verse 4)
God will indeed be their enemy wherever they turn. Such a prayer by God Almighty means a verdict that is certain to take place. It is their inevitable outcome, as history has clearly shown.” 
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 Sayyid Abul Ala Maududi:
“As we shall explain below this Surah was sent down either during the Holy Prophet’s return journey from his campaign against Bani al- Mustaliq, or immediately after his arrival back at Madinah, and we have established by argument and research in the Introduction to Surah An-Nur that the campaign against Bani al-Mustaliq had taken place in Sha’ban A. H. 6:Thus, the date of the revelation of this Surah is determined precisely.” (Sayyid Abul Ala Maududi – Tafhim al-Qur’an – The Meaning of the Qur’an – Period of revelation – Online source)
 The Holy Qur’an – Arabic Text With English Translation & Short Commentary By Malik Ghulam Farid, Page 1140
 The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction by Maulana Muhammad Ali, page 1094 – 1095
 The Message of The Quran translated and explained by Muhammad Asad, page 1176
 In the Shade of the Qur’an By Sayyid Qutb volume 17, Page 27 – 28