Wiktionary
n. (context Roman Catholicism English) An auxiliary bishop with the right of succession, i.e., he becomes bishop upon the death, removal or retirement of the incumbent bishop.
Wikipedia
A coadjutor bishop (or bishop coadjutor) is a bishop in the Roman Catholic or Anglican churches who is designated to assist the diocesan bishop in the administration of the diocese, almost as co-bishop of the diocese. The coadjutor (literally, "co-assister" in Latin) is a bishop himself, and while also appointed as vicar general, is given authority beyond that ordinarily given to the vicar general, making him co-head of the diocese in all but ceremonial precedence. In modern times, the coadjutor automatically succeeds the current bishop of a diocese upon the latter's retirement, removal or death.