I hear this term thrown around a lot, in connection to a variety of different works. They don't all share the same central themes, though - at least not necessarily. But they do all tend to be connected in a pretty basic way: they're all fairly grim.
Online definitions circularly say that "Dostoevskian" means "in the style of Fyodor Dostoevsky," which isn't particularly helpful.
What aspects of his works are typically specifically referred to by this term? Do people mean to say that a work is nihilistic, or explores seemingly irrational behavior? Or do they mean something else entirely?