By the star when it goes down, (or vanishes).

your companion (Muhammad) is neither astray, nor misguided,
Meaning:-
Astray: into error, away from the correct path or direction

Nor does he speak of (his own) desire

This Qur’an is but an inspired revelation.
Meaning:-
Inspired: of extraordinary quality, Outstanding or brilliant in a way or to a degree suggestive of divine inspiration.

He is being taught by one who is mighty, powerful (angel Gabriel);

Owner of resolute splendor; (Literally: ability to transform; to convey revelation, i.e. Jibril “Angle Gabriel) so he leveled himself.
Meaning:-
Resolute: admirably purposeful, determined, and unwavering.
Splendor: magnificent features or qualities.

While he [Jibrael (Gabriel)] was in the highest part of the horizon,
Meaning:-
Horizon: the limit or range of knowledge, understanding, or experience.

Then he [Jibrael (Gabriel)] approached and came closer,

within the length of two bows or even closer,

and revealed to Allah’s servant [Muhammad through Jibrael (Gabriel) ] that what he was supposed to reveal.

His (Muhammad’s) own heart did not deny that which he saw.

Will you then dispute with him (Muhammad) about what he saw [during the Mi’raj: (Ascent of the Prophet over the seven heavens)].

And indeed he (Muhammad) saw him [Jibrael (Gabriel)] at a second descent (i.e. another time).

near Sidra-tul-Muntaha (the Lot-tree at the farthest end of the seven heavens, beyond which none can pass).
Meaning:-
Lote tree may refer to: Sidrat al-Muntaha, the tree that marks the end of the seventh heaven, the boundary where no creation can pass, and beyond which is the Throne of Allah,

Near it is Janna-tul-M’awa (the rest-house of paradise).

When that Lot-tree was covered with what covered it,
Meaning:-
Lote tree may refer to: Sidrat al-Muntaha, the tree that marks the end of the seventh heaven, the boundary where no creation can pass, and beyond which is the Throne of Allah,

The sight [of the Prophet] did not swerve, nor did it transgress [its limit].
Meaning:-
Swerve: to turn aside abruptly in movement or direction; deviate suddenly from the straight or direct course.
Transgress: break the law, wrongdoing, disobey.

Indeed he (Muhammad) did see, of the Greatest Signs, of his Lord (Allah).

Have you then considered Al-Lat, and Al-‘Uzza (two idols of the pagan Arabs).
Meaning:-
Al-Lat, and Al-‘Uzza: Three of them are referred to as the daughters of Allah. The Goddesses Al-Uzza, Al-Lat and Menat was most venerated Arab Deities. They were widely worshipped, and the three of them were very popular Goddesses in Mecca at the time of prophet Mohammed (PBUH).
Pagan: is a person who worships many gods or who worships nature and the Earth

and another, the last third Manat (names of Arabian idols, claimed by the pagans of Makkah to be the daughters of Allah)?
Meaning:-
Al-Uzza, Al-Lat and Menat (Arab Deities) : Three of them are referred to as the daughters of Allah. The Goddesses Al-Uzza, Al-Lat and Menat was most venerated Arab Deities. They were widely worshipped, and the three of them were very popular Goddesses in Mecca at the time of prophet Mohammed (PBUH).

Is the male for you and for Him the female?

This indeed is an unfair division!

These (Lat, Uzza and Manat) are nothing but names which you and your forefathers have invented, for Allah has vested no authority in them. The unbelievers follow nothing but mere conjecture and the whims of their own souls, even though right guidance has already come to them from their Lord.
Meaning:-
Al-Uzza, Al-Lat and Menat (Arab Deities) : Three of them are referred to as the daughters of Allah. The Goddesses Al-Uzza, Al-Lat and Menat was most venerated Arab Deities. They were widely worshipped, and the three of them were very popular Goddesses in Mecca at the time of prophet Mohammed (PBUH).
vested:held completely, permanently.
Conjecture: speculation, guesswork, assumption.
Whim: a sudden wish or idea, especially one that cannot be reasonably explained

Or should man have whatever he wishes?

Nay! To Allah belongs the hereafter and this present life.

And how many an angel is there in the heavens whose intercession does not avail at all except after Allah has given permission to whom He pleases and chooses.
Meaning:-
Intercession: prayer, petition, or entreaty in favor of another.

Indeed, those who do not believe in the Hereafter name the angels female names,

While they have no knowledge thereof. They follow but a guess, and verily, guess is no substitute for the truth.

Therefore withdraw (O Muhammad) from him who turns away from Our Reminder (this Quran) and desires nothing but the life of this world.

This is the sum of their knowledge. Surely your Lord knows who have strayed from His path, and who are rightly guided.
Meaning:-
Stray: to go astray; deviate, to deviate from the direct course.

And to Allah belongs all that is in the heavens and all that is in the earth, that He may recompense those who do evil with that which they have done (i.e. punish them in Hell), and reward those who do good, with what is best (i.e. Paradise).

Those who avoid the major sins and immoralities, only [committing] slight ones. Indeed, your Lord is vast in forgiveness. He was most knowing of you when He produced you from the earth and when you were fetuses in the wombs of your mothers. So do not claim yourselves to be pure; He is most knowing of who fears Him.
Meaning:-
Immorality: corruption, dishonesty, character, or conduct; wickedness; evilness and sexual misconduct.

Have you seen the one who (Walid bin Mughirah, who was willing to embrace Islam, but upon someone’s promise to take the responsibility of getting the punishment on his behalf in lieu of certain amount of money, he) turned away.
Meaning:-
Lieu: instead, in place of.

He gave a little from the promised amount then stopped.

Does he possess the knowledge of the unseen that he could see reality?

Or has he not been informed of what was in the scriptures of Moses

and of Ibrahim (Abraham) who always kept his word:

“That no soul shall bear the burden of another,

And that man can have nothing but what he does (good or bad).

And that his deeds will be seen,

that he shall be fully rewarded for it,

that to your Lord is the final goal,

And that it is He (Allah) Who makes (whom He wills) laugh, and makes (whom He wills) weep;
Meaning:-
Weep: cry, shed tears.

And that it is He (Allah) Who causes death and gives life;

And that He (Allah) creates the pairs, male and female,

from a drop of ejaculated semen,

that it rests upon Him to grant the second life (the life of hereafter),

that it is He Who gives wealth and property,

that He is even the Lord of the Sirius (dog star whom the pagans Arabs used to worship),
Meaning:-
Sirius: the Dog Star, the brightest-appearing star in the heavens, the brightest star in the Earth’s night sky.
Pagan: is a person who worships many gods or who worships nature and the Earth

And that it is He Who destroyed the (powerful) ancient ‘Ad (people),

then the people of Thamud, sparing no one,

and before them the people of Nuh (Noah), who were the most unjust and rebellious.
Meaning:-
Rebellious: disobedient, insubordinate.

And He destroyed the overthrown cities [of Sodom to which Prophet Lout (Lot) was sent].

So there covered them that which did cover (i.e. torment with stones).
Meaning:-
Torment: torture, pain, severe physical or mental suffering.

Then which of your Lord’s blessings would you doubt?

This (Muhammad) is a warner (Messenger) of the (series of) warners (Messengers) of old.

The ever approaching (the Day of Judgement) is drawing near;

none but Allah can disclose it.

Do you then wonder at this revelation,

and laugh instead of weeping?

Rather you are wasting your time,

prostrate yourselves before Allah and worship Him while you can!
Meaning:-
Prostrate: lying stretched out on the ground with one’s face downward, especially in reverence or submission.