A rabbi is not a priest, neither in the Jewish sense of the term nor in the Christian sense of the term. In the Christian sense of the term, a priest is a person with special authority to perform certain sacred rituals.
A rabbi, on the other hand, has no more authority to perform rituals than any other adult male member of the Jewish community. In the Jewish sense of the term, a priest (kohein) is a descendant of Aaron, charged with performing various rites in the Temple in connection with religious rituals and sacrifices. Although a kohein can be a rabbi, a rabbi is not required to be a kohein.
A rabbi is simply a teacher, a person sufficiently educated in halakhah (Jewish law) and tradition to instruct the community and to answer questions and resolve disputes regarding halakhah. When a person has completed the necessary course of study, he is given a written document known as a semikhah, which confirms his authority to make such decisions.