It's his personal study on human nature fictionalized as a mundane story. The meat of the work isn't the plot, but the interactions between the characters, which each are supposed to represent various personality archetypes and world-views they subscribe to.

It's also interesting to consider each character (disregarding minor characters) all of as an orthogonal dimension of a single person (by no means scientific): the inner-monkey (Dmitri), hyper-intellect (Ivan), spiritual/altruistic (Alyosha). From this perspective, the work is a solipsistic study on how inner-conflict manifests outwardly into the world.