The legal parent is a parent that has a legally established parent-child relationship with their child. If you are the legal parent of a child, your name likely will or otherwise can be placed on that child's birth certificate.
A child's legal parent is allowed to do the following:
make or receive child support payments, depending on their relationship with the child
pursue getting custody of a child
pursue parenting time (visitation rights) with a child
Depending on how one's legal parentage was originally established, one can possibly become no longer recognized as the child's legal parent through one of the following ways:
a denial of parentage; or