Refers to a person who makes a request or petition, often in a formal or religious context. The 'prayer' sense is literal, as in one who prays at a shrine or temple.
The supplicant prayed for family safety at the shrine.
この奨学金の願い主は毎年増えている。
The number of applicants for this scholarship is increasing every year.
Compound of 願い (negai, 'wish, request') and 主 (nushi, 'master, owner, person'). The exact historical derivation is uncertain, but the word literally means 'the person of the request'.