A more thorough explanation:

A contestant is someone who participates in a competition or challenges an award or person. In child custody cases, a contestant is a person, including a parent, who claims the right to custody or visitation of a child.

• Athletes who compete in the Olympics are contestants.
• In a singing competition, the singers are contestants.
• In a child custody case, both parents can be contestants if they both claim the right to custody or visitation of the child.

The examples illustrate that a contestant is someone who is actively participating in a competition or contest. In the context of child custody cases, a contestant is someone who is claiming the right to custody or visitation of a child, and is therefore involved in a legal contest.