Baptism is a Christian sacrament, and the theology of it is that it removes original sin. The child, once baptised, becomes a Christian and can enter into eternal life.
Some Protestants challenged infant baptism, at the time of the Reformation, saying that it ought to be a choice taken by an adult (as it seems to have been in Gospel accounts.)
There are Protestant sects such as the Quakers, who do not believe in baptism, or any other sacrament.
The Eastern Orthodox Christians do not hold to the doctrine of original sin, therefore see baptism having a different significance - of welcoming the child into the church community, and santifying it. But in their view, the child was not damned by original sin before the ceremony.
The baptisms in Gospel narratives were closely related to the Jewish practice of immersion in pure water, as a gesture of repentance from sin and rededication for prayer. If continued in this form, baptism would have become a practice whereby Christians practiced it often throughout their lives. But that faded out, and it became a single ritual performed by the clergy.
>>Some Protestants challenged infant baptism, at the time of the Reformation, saying that it ought to be a choice taken by an adult (as it seems to have been in Gospel accounts.) <<
There is no such assertion in the bible that baptism was an adult choice. Naturally, since the key characters in the New Testament are all adults, the stories about baptism revolve around adults. But when the leader of a household was baptized, his entire household was baptised with him. It would be inconceivable that an entire household would include no children, for a household included not only the nuclear family, but also in-laws, kinfolk, slaves, and all their children! There is no chance that there were no children baptized.
A child becomes a Christian at baptism!? Amazing.