How does the dot product $F(x) \cdot n(x)$ give the vector components on the surface

Question

Let $F$ be some vector field (say in $\mathbb R^{3})$ and $n$ be the unit vector of the surface. How exactly does $F(x) \cdot n(x)$ (where $\cdot$ is the dot product) give the vector component ("normal component") on the surface needed to calculate the flux in an area $dS$? Is the normal component (let's call it $h(x)$) basically the horizontal component of $F(x)$so that $n(x)$ and $h(x)$ added together will give us $F(x)$. I am confused!