There are many recurring themes throughout Judaism. It is easy to discover some of these themes, like the repetition of the number forty. In order to receive the Torah, Moshe stayed on Har Sinai for forty days, חטא המרגלים (the sin of the spies) left Bnei Yisrael in the desert for forty years, etc... Likewise, there are many parallels between different holidays throughout the Jewish calendar. In fact, the calendar can be cut in half thematically so that the months of Nisan and Elul both begin new sub-years of their own.
Starting with Elul, Bnei Yisrael go through a period of spiritual rise. Elul begins the process which culminates at Yom Kippur, which is ten days after the birth of the world, Rosh Hashana. These ten days are those of the most intense Teshuvah. After we have attained the high level of Kedushah associated with Ne'ilah, we immediately begin our preparations for, and celebration of, Succot, the ultimate holiday of Simcha, joy. The same pattern is seen beginning with Pesach. Bnei Yisrael are "born" as a nation upon leaving Egypt, and go through a spiritual rise until they reach a highest level of receiving the Torah on Shavuot. Shavuot is also a time of great spiritual Simcha. These two periods of the year are therefore closely related.
The time of year around Tishrei is often considered the primary time for Teshuvah and returning to Hashem. However, it is obvious that the period which we are in now is similar to it, and therefore must not be wasted by procrastination until Yom Kippur to better ourselves. We must make sure that this Shavuot brings us to new heights so that by the time Yom Kippur does come around it won't be as crucial for Teshuvah as it otherwise would be. In this way we will be able to use it to soar to even greater levels of spirituality and קדושה (holiness).