The word tzom first appears in the book of Shoftim, when the Bnei Yisrael fast during their ongoing – and failing – civil war with the tribe of Binyamin. It seems to be a means of repentance. It next appears in the book of Shmuel, once again for the purpose of teshuvah.
The next time that this word appears, however, is when the body of Shaul was captured by the Plishtim in battle. Then, the men of Yavesh Gilad go on a rescue mission to recover his body along with those of his sons. When they returned successfully, they fasted for seven days. In the first two cases, the people fast so as to come near to Hashem in teshuvah. In the third case, they appear to mourn out of closeness with Shaul, with whom they feel a special connection.
Fasting, then, is an expression of closeness – achieved or desired. And when we think about it, isn’t that really the point of all of our own fasts as well?