There is a general notion of a geometric point in topos theory. A geometric point is a geometric morphism $Set\to T$.

There is also a notion of a geometric point in algebraic geometry. A geometric point is a point $k\to S$ where $k$ is algebraically closed.

Why do these notions agree?

The geometric points of the étale site of a scheme are maps $k\to S$ where $k$ is separably closed. Again, why are these the same as geometric morphisms from the category of sets into the étale topos?