Then John gave this testimony: “I saw the Spirit come down from heaven as a dove and remain on him".
The Spirit has no bodily form and we cannot see him, but as the synoptic Gospels make clear, the baptism of Jesus was accompanied by an actual dove alighting on Jesus and remaining for a little while. This is a symbol for the Spirit's anointing, pointing out that Jesus was in fact divine. It isn't clear why God chose a dove to represent the Spirit, though secular humanists today often make use of the dove to represent what they mean by spirituality.
When Jesus began his ministry he quoted from Isaiah 61:1-2 The “The Spirit of the Lord is on me, because he has anointed me to proclaim good news to the poor.
He has sent me to proclaim freedom for the prisoners and recovery of sight for the blind, to set the oppressed free, to proclaim the year of the Lord’s favor.”
This anointing meant both that Jesus had been chosen by God to carry out a specific task and that he was qualified to do so.