In Federation society, a legal guardian was a person responsible for a person unable to be operate as a responsible adult themselves. They were tasked with making decisions and looking after those persons, with their best interest in mind. The person they were responsible for was called their legal ward.
In 2269, Flint claimed Rayna Kapec was placed into his custody as a legal ward after her parents died. However, no record of this could be found in the Federation legal banks. (TOS: "Requiem for Methuselah")
In 2375, Starfleet psychiatrist Karen Loews was the legal guardian of Sarina Douglas, and in that capacity was able to approve an experimental medical procedure for her. (DS9: "Chrysalis")