I'm sorry if my question is rather trivial, but I'm starting to learn scheme theory and I have a very basic question.
When talking about schemes I see that very often, instead of taking "a point of a scheme $X$", is customary to take a $T$-point of $X$ (where $T$ is another scheme) i.e. a morphism $T\rightarrow X$. In this way, under the hypothesis that both $X$ and $T$ are schemes over a field $k$, we obtain a scheme $X\times_k T$ over $T$ (this is also called "base change" as I understand). My question is: why is this "relative setting" so useful and so what is the importance of the $T$-points? In other words, why can't we just consider usual points, as we do for topological spaces or complex varieties?
Thank you very much.