1)    On the thirty third day of the omer, we slightly increase our happiness, as on that day the students of Raabi Akiva stopped dying. (Even according to the opinion of the Shulchan Aruch and the custom of the Sephardim who permit haircutting etc. only from the thirty fourth day, that is because the main stopping of death was on the thirty third, but there were still a few deaths on the thirty fourth.) (Shulchan Aruch and Mishne Berurah 493)

2)    There are some who say that the reason for the happiness is because after this Rabbi Akiva taught another five students (one of whom was Rabbi Shimon Bar Yochai) who did not die like their predecessors, but taught Torah to all of Klal Yisrael. (Peri Chadash)