The rabbi might quote a passage from the Torah that's relevant to the occasion and to the particular couple. Or he might not.
His purpose in being there is to monitor the proceedings, make sure that the elements required by Jewish law are included in the ceremony and are properly performed; and to simultaneously fulfill the requirement for the presence of a government-recognized wedding-officiator.
Nothing that the rabbi says or doesn't say during the wedding ceremony either makes the wedding official or prevents it from becoming official. The Jewish bride and groom marry each other; the rabbi doesn't marry them.
At a traditional wedding, the Rabbi reads the Ketubah (wedding contract) under the wedding canopy, as part of the ceremony.