In Suikoden, the 108 Stars of Destiny refers to the protagonist and the other 107 characters who will aid him (usually) at his headquarters in his epic struggle with fate.
In each main Suikoden game (excluding the Genso Suikogaiden games and Suikoden Tactics), there are 108 recruitable characters. While recruiting all of the Stars of Destiny is not a requirement to finishing the game, recruiting all of them gives certain bonuses that affect the story of the game.
Origin of the 108 Stars
The 108 Stars of Destiny likely comes from the Legend of the 108 Stars of Destiny from the Chinese Novel, Shui Hu Zhuan ("Water Margin"). The 108 Stars are broken down into 36 Stars of Heaven, or 36 Heavenly Spirits, and 72 Stars of Earth, or 72 Earthly Warriors.
List of Stars
At some point in every game, the protagonist will acquire the Tablet of Stars which lists the names of all of the stars, in addition to the names of the characters who have joined that are associated with them, and whether or not those characters are alive.
36 Stars of Heaven