Verse 13 tells us that the parents wanted Jesus to touch their children. This is further explained in verse 16, where Jesus places his hands on the children, touching them and blessing them. Thus, the parents wanted Jesus to bless their children.
It seems to have been a practice at the time of the New Testament that some rabbis were asked to bless children. This would involve them praying a blessing similar to Numbers 6:24–26 upon the child. Parents probably thought that the prayers of such a person were more effective or powerful than their own.
The parents bringing their children to Jesus know that he is someone with great wisdom (Mark 1:27) who is also able to heal and cast out demons (Mark 3:10–12). They recognize that he must be a prophet from God (Mark 8:27–28). Knowing these things about Jesus, the parents trust that he lives in close relationship with God and that a prayer of blessing from him on behalf of their child will stand their child in good stead for the future.
13 And they were bringing children to him that he might touch them, and the disciples rebuked them.