All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Shams-ul-Haqq Abaadi Al-Hindi wrote about the explanation of these phrases: “The phrase ‘I am content with Allaah as my Lord,’ means that I am content with Allaah Who is characterized by His lordship and all His decrees and what He has predetermined. It is also said to mean that I am content with Allaah as my educator, king, master and caretaker. The phrase, ‘I am content with Muhammad as my Messenger,’ means that I am content with his entire message and all of the matters of doctrine and everything else that he has delivered. The phrase, ‘I am content with Islam,’ means that I am content with all of the laws of Islam, namely what is commanded and forbidden, '...as a religion,' that is, as a belief and practice.” [‘Awn Al-Ma‘bood fi Sharh Sunan Abu Daawood]
This is a brief explanation of the phrases.
For more benefit, please refer to Fatwa 89000.
Allaah Knows best.