I have read and understood the definition of the pushforward of a $\mathcal{D}_X$-module $\mathcal{M}$ under a morphism of varieries $$f:X\longrightarrow Y$$ In particular, if $Y=\{ \star \}$ is a point and $\mathcal{M}=\mathcal{O}_X$ then $$f_* \mathcal{O}_X= \ \ \ \left( H^n(X) \to \cdots \to H^0(X) \right)$$ is the de Rham cohomology complex of X.
However, I don't know why this should be true. Can anyone explain why, before reading the definition of a pushforward, one would guess this as the only possible reasonable answer?
(Maybe part of the problem is that I've not got a good picture of what this process is meant to be doing geometrically).