The Ramban (Vayikra 23, 28) points out that in the portion of the Torah dealing with Shabbos and Yom Tov, the terminology of "b'etzem hayom hazeh" (in the midst of this very day)is used only with regard to the Yamim Tovim of Yom Kippur and Shavuos. The Ramban explains with regard to Yom Kippur, that Chazal tell us this terminology reflects the fact that the day itself has the ability to bring about atonement.
Rav Wolbe (Shiurei Chumash) elaborates that Yom Kippur is a Yom Tov which is unique in the aspect that there is no mitzvah that requires a physical action accompanying the day. On Rosh Hashana we blow the shofar, on Sukkos we shake the arba'a minim and sit in the Sukkah, and on Pesach we eat matzah. In contrast Yom Kippur is a day which depends a great deal on the way one feels in his heart. Repentance, which is made up of feelings of regret and a genuine commitment to depart from one's misdeeds, is effective to the degree one truly feels these feelings inside his heart. The day itself has a special potency, but we must also do teshuva in our hearts. To some extent, this helps us define the difficulty that some may have with properly connecting to this holiest day of the year.
This same idea holds true for the Yom Tov of Shavuos: there is no physical mitzvah pertaining to the day. Rather, we are to renew our commitment to study Torah and keep the mitzvos - a task that cannot be accomplished with our hands but rather with our hearts. It is a special day as long as we take its theme to heart.
As Chazal tell us, "Rachmana leeba ba'ee." Hashem desires sincere service; service that includes feelings deep within one's heart. Yom Kippur and Shavuos are two days that, if utilized properly, can significantly change a person for the better. Incidentally, acknowledging that sincere repentance and a serious commitment to Torah can only be accomplished with a heartfelt decision, will aid us in our performance of all mitzvos. We will realize that they too, to a great extent, depend upon the amount of "heart" we put into them.