Jesus is the epitome of the righteous example in all things. He set us an example to follow with regard to the process of our conversion as well. Though He committed no sins to be remitted, He was baptized, setting the example for us. Matthew 3:13-17 describes the account of His baptism by John the Baptizer.
In being baptized, Jesus was immersed in water (not sprinkled or poured upon). We know from the Gospel account that,
So, He came up out of the water because He was under the water, so that His sins would be symbolically washed away, not His sins but our sins because He was only symbolically doing it to show us an example. He had no sin to be washed away.
Not only did Jesus set the example by personally being baptized, He also baptized more disciples than John the Baptist did.
The purpose of Jesus' baptism was to set us an example. He was put down into the water, for He went up out of the water. Both Philip and the eunuch went down into the water. There was no reason for Philip to go actually into the water, except for the reason there was no other way he could plunge the eunuch into the river. "They came up out of the water together" is the way that it is worded.