Allah says:
{Those to whom We have given the Book}

and who recite it as it should be recited, including the Jews and Christians,
{rejoice at what has been revealed unto you,}

i.e. the Qur'an, because they have evidence in their Books affirming it and delivering the good news of its coming. Allah said in other Ayat,
{Those to whom We gave the Book. And they recite it as it should be recited, they are the ones who believe therein.} [2:121], and,
{Say: "Believe in it (the Qur'an) or do not believe."} [17:107], until,
{Truly, the promise of our Lord must be fulfilled.} [17:109]
meaning, Allah's promise to us in our Books to send Muhammad is true. It is certain and will surely come to pass and be fulfilled, so all praise to our Lord, how truthful is His promise, all the thanks are due to Him,
{And they fall down on their faces weeping and it increases their humility.} [17:109]
Allah said next,
{but there are among the Ahzab (Confederates) those who reject a part thereof.}

meaning, 'There are those among the sects who disbelieve in some of what was revealed to you (O Muhammad).' Mujahid said that,
{but there are among the Ahzab (Confederates)}, refers to Jews and Christians,
{those who reject a part thereof}, meaning, 'They reject a part of the truth that came down to you - O Muhammad.' Similar was reported from Qatadah and 'Abdur-Rahman bin Zayd bin Aslam. Allah said in similar Ayat,
{And there are, certainly, among the People of the Scripture, those who believe in Allah and in that which has been revealed to you, and in that which has been revealed to them.} [3:199]
Allah said next,
{Say: "I am commanded only to worship Allah and not to join partners with Him.}

meaning: I was sent with the religion of worshiping Allah alone without partners, just as the Messengers before me,
{Unto Him (alone) I call}

I call the people to His path,
{and to Him is my return.}

my final destination and return. Allah's statement,
{And thus have We sent it (the Qur'an) down to be a judgement of authority in Arabic.}

means, 'Just as We sent Messengers before you and revealed to them Divine Books from heaven, We sent down to you the Qur'an, a judgement of authority in Arabic. We honored you with the Qur'an, which is a clear, plain, unambiguous Book that leaves no excuse and defies any opponent.'
{Were you to follow their desires}

meaning, their opinions,
{after the knowledge which has come to you,}

from Allah, all praise to Him,
{then you will not have any Wali (protector) or defender against Allah.}

This part of the Ayah warns people of knowledge against following the paths of misguidance after they had gained knowledge in (and abided by) the Prophetic Sunnah and the path of Muhammad, may Allah's best peace and blessings be on him.