I never understood the Baptism of Christ, since he is sinless and born of a sinless mother. Please explain.

It is clear, that Jesus was without sin (e.g., Heb 4:15). Even as Jesus approaches John for baptism, John instinctively protests. However, the Lord explains, saying, Let it be now so in order to fulfill all righteousness (Matt 3:15). 
 
Jesus is referring to the righteousness (justice) of God. God’s justice is his fidelity to his promises. And God had promised to send us a Messiah to go ahead of us and lead us out of sin, and into righteousness. 
 
At the River Jordan, Jesus is like Moses, who did not just tell the people to cross the Red Sea, he went ahead, courageously leading them through the stormy waters. Jesus does no less. And does not tell us merely to go to the waters of baptism; he leads us through baptism, out of slavery, into freedom. 
 
The liturgy of the Church speaks of Jesus not being made holy by the waters, but making the waters holy to bless us. 
 
Jesus also does this with the “baptism” of the whole Paschal mystery. He does not merely tell us to take up a cross, he takes up his cross and bids us follow him. He does not merely point to the hill of Calvary; he leads us up over that hill and unto glory. 
 
This is God's righteousness, his justice, this is his fidelity to his promises. 
 
Another aspect of Jesus’ baptism is the remarkable fact that he identifies with sinners, though he himself is not a sinner. He is not ashamed to call us his brethren (Heb 2:11). He who was sinless, was seen as a great sinner, and crucified publicly. Such love, such emptying, such humility. For the Lord conquers Satan's pride, and ours, by astonishing humility. And in this too, Jesus “fulfills all righteousness” by being Baptized, going into the waters ahead of us.