The Gemara says (Megillah 31B): “We read the klalos in Toras Kohanim (Parshas Bechukosai) before Atzeres (Shavuos), and those in Mishnah Torah (Parshas Ki Savo) before Rosh Hoshanah so that the year and its curses should end and a new year and its blessing should begin.” The Gemara asks that it is understandable how this applies to Rosh Hashanah, but what does this have to do with Shavuos? It answers that Shavuos is also a “New Year”, as the fruits of the tree are judged on Shavuos.
We see from this Gemara that Shavuos is called “Rosh Hashanah”. The Meor Vashemesh (Parshas Bechukosai) explains that just like the period before Rosh Hashanah is a time for teshuva, as the judgment is approaching and we need Hashem to forgive our sins and decree upon us a good year, so too the days of Sefirah that precede Shavuos are a time to repent and return to Hashem. If we do this, Hashem will forgive our sins on Shavuos and grant us a New Year of blessing.