Encouraging the Children of Israel to embrace Islam 

Allah says; 

يَا بَنِي إِسْرَايِيلَ

O Children of Israel!

Allah commanded the Children of Israel to embrace Islam and to follow Muhammad. He also reminded them with the example of their father Israel, Allah's Prophet Yaqub, as if saying, "O children of the pious, righteous servant of Allah who obeyed Allah! Be like your father, following the truth."

This statement is similar to one's saying, "O you son of that generous man! Do this or that," or, "O son of the brave man, engage the strong fighters," or "O son of the scholar, seek the knowledge," and so forth. Similarly, Allah said,

ذُرِّيَّةَ مَنْ حَمَلْنَا مَعَ نُوحٍ إِنَّهُ كَانَ عَبْدًا شَكُورًا

O offspring of those whom We carried (in the ship) with Nuh (Noah)! Verily, he was a grateful servant. (17:3)
Israel is Prophet Yaqub (Jacob) 

Israel is Prophet Yaqub, for Abu Dawud At-Tayalisi recorded that Abdullah Ibn Abbas said,

"A group of Jews came to the Prophet and he said to them,

هَلْ تَعْلَمُونَ أَنَّ إِسْرَايِيلَ يَعْقُوبُ
 
 

Do you know that Israel is Jacob?

They said, "Yes, by Allah."

He said,

اللَّهُمَّ اشْهَد

O Allah! Be witness."

At-Tabari recorded that Abdullah Ibn Abbas said that;

`Israel' means, `the servant of Allah.'
Allah's Blessings for the Children of Israel 

Allah said,
 
اذْكُرُواْ نِعْمَتِيَ الَّتِي أَنْعَمْتُ عَلَيْكُمْ

Remember My favor which I bestowed upon you.

Mujahid commented,

"Allah's favor that; 

He granted the Jews is that He made water gush from stones, 

sent down manna and quails for them, 

and saved them from being enslaved by Pharaoh." 

Abu Al-Aliyah also said,

"Allah's favor mentioned here is His sending Prophets and Messengers among them, and revealing Books to them."

I - Ibn Kathir - say that this Ayah is similar to what Musa said to the Children of Israel,

يَـقَوْمِ اذْكُرُواْ نِعْمَةَ اللَّهِ عَلَيْكُمْ إِذْ جَعَلَ فِيكُمْ أَنْبِيَأءَ وَجَعَلَكُمْ مُّلُوكاً وَءَاتَـكُمْ مَّا لَمْ يُوْتِ أَحَداً مِّن الْعَـلَمِينَ

O my people! Remember the favor of Allah to you:when He made Prophets among you, made you kings, and gave you what He had not given to any other among the nations (of their time. (5:20),

meaning, during their time.

Also, Muhammad bin Ishaq said that Ibn Abbas said, 
اذْكُرُواْ نِعْمَتِيَ الَّتِي أَنْعَمْتُ عَلَيْكُمْ
 (Remember My favor which I bestowed upon you), means,

"My support for you and your fathers,"

that is saving them from Pharaoh and his people.
Reminding the Children of Israel of Allah's Covenant with Them 

Allah's statement,
 
وَأَوْفُواْ بِعَهْدِي أُوفِ بِعَهْدِكُمْ

And fulfill (your obligations to) My covenant (with you) so that I fulfill (My obligations to) your covenant (with Me),

means, `My covenant that I took from you concerning Prophet Muhammad, when he is sent to you, so that I grant you what I promised you if you believe in him and follow him. I will then remove the chains and restrictions that were placed around your necks, because of the errors that you committed.'

Also, Al-Hasan Al-Basri said,

"The `covenant' is in reference to Allah's statement,

وَلَقَدْ أَخَذَ اللَّهُ مِيثَـقَ بَنِى إِسْرَءِيلَ وَبَعَثْنَا مِنهُمُ اثْنَىْ عَشَرَ نَقِيباً وَقَالَ اللَّهُ إِنِّى مَعَكُمْ لَيِنْ أَقَمْتُمُ الصَّلوةَ وَءَاتَيْتُمْ الزَّكَوةَ وَءَامَنتُمْ بِرُسُلِى وَعَزَّرْتُمُوهُمْ وَأَقْرَضْتُمُ اللَّهَ قَرْضاً حَسَناً لاُكَفِّرَنَّ عَنْكُمْ سَيِّيَـتِكُمْ وَلادْخِلَنَّكُمْ جَنَّـتٍ تَجْرِى مِن تَحْتِهَا الاٌّنْهَـرُ

Indeed, Allah took the covenant from the Children of Israel (Jews), and We appointed twelve leaders among them. And Allah said:"I am with you if you perform As-Salah and give Zakah and believe in My Messengers; honor and assist them, and lend a good loan to Allah, verily, I will expiate your sins and admit you to Gardens under which rivers flow (in Paradise)." (5:12) 

Other scholars said,

"The covenant is what Allah took from them in the Tawrah, in that, He will send a great Prophet - meaning Muhammad - from among the offspring of Ismail, who will be obeyed by all peoples. Therefore, whoever obeys him, then Allah will forgive his sins, enter him into Paradise and award him two rewards."

We should mention here that Ar-Razi mentioned several cases of information brought by the earlier Prophets regarding the coming of Muhammad.

Further, Abu Al-Aliyah said that, 
وَأَوْفُواْ بِعَهْدِي
 (And fulfill (your obligations to) My covenant (with you)) means,

"His covenant with His servants is to embrace Islam and to adhere to it."

Ad-Dahhak said that Ibn Abbas said,

"`I fulfill My obligations to you' means, `I (Allah) will be pleased with you and admit you into Paradise."'

As-Suddi, Ad-Dahhak, Abu Al-Aliyah and Ar-Rabi bin Anas said similarly.

Allah's statement,
 
وَإِيَّايَ فَارْهَبُونِ
 
 

And fear Me and Me alone.

Ibn Abbas said that it means,

"Fear the torment that I might exert on you, just as I did with your fathers, like the mutation, etc."

This Ayah contains encouragement, followed by warning. Allah first called the Children of Israel, using encouragement, then He warned them, so that they might return to the Truth, follow the Messenger, heed the Qur'an's prohibitions and commands and believe in its content. Surely, Allah guides whom He wills to the straight path.

Allah said next