How do you drive story in a game? How do you inject a bit of conflict between characters who would otherwise co-operate? How do you bring a bit of co-operation between characters who might otherwise be constantly at one another's throats?
A simple answer to all of these questions comes in the form of factions, and many games have made use of this idea.
From the clans of Vampire the Masquerade or Legend of the Five Rings, the orders of Magi in Ars Magica, the corporations in assorted cyberpunk games or even the chapters of Space Marines in Warhammer 40,000.
Factions add instant ties between characters, whether those ties come in the form of communion or conflict.
Of course, factions don't always make a game better, in the same way that conflict doesn't always make a story better. Many kung fu movies are great because they bring creative conflict to the screen, but few kung fu movies are considered masterpieces of storytelling.
Like all mechanisms, you need to consider what you want the outcome to be, and how the mechanism plays toward that outcome.