"My Father has entrusted all things to me" or "My Father has given everything over to me." This could mean that 1) God the Father has revealed everything about himself and his kingdom to Jesus or 2) God has given all authority to Jesus.
These are important titles that describe the relationship between God and Jesus. It is best to translate “Father” and “Son” with the same words that your language uses to refer to a human father and a human son. The word "knows" here means more than just being acquainted with someone. It means knowing someone intimately because of having a special relationship with him.