They generally announce to the reader the beginning of a new story arc. I think that's about all there is to it. The format of a sequence of short story arcs that combine more or less loosely to form a larger story arc has become something of a TV staple since BTVS popularized it. But it has existed in fiction for a long time. LOTR is an obvious example. Indeed, you can find arcs within arcs within arcs in LOTR. Lots of Dickens is similar. I suspect most long works are.
When we talk about story shapes we tend to focus on the shape of an individual story arc, which is an appropriate thing to do for analytical purposes. But a novel is a much more complex work of art than the shape of a single story arc suggests, and may include many arcs, either in parallel or in serial or both. Dividing a work into parts is a way of indicating the transition from one serial arc to another.
In a complex work, you have to give the reader adequate clues that you have shifted in time or character or arc, and this is just one way to do it. But I would regard is very much as a tool you can use, not a rule you must follow.