A proselyte is a new convert, especially someone who has recently switched from one religion to another. In some Christian churches, a proselyte must be baptized.
You can use the word proselyte to talk about any kind of convert, even those that aren't religious. You could, for example, call your brother a proselyte if he voted for a Republican in the last election but recently joined the Democratic party. The most common use of the word, however, is someone who converts to Judaism. Proselyte has a Greek root, proselytos, which means both "convert to Judaism" and "one who has come over."