Expressing a reflected ray at a point as a function of the incoming ray and the normal to the surface at that point
$N \cdot L$ is the scalar length of the projection of $L$ on $N$ (assuming $|N|=1$).

$(N \cdot L)N$ is the actual vector with the length of $N \cdot L$ in the direction of $N$.

There is often a confusion when people say "projection of this on that" whether they mean just its length, or the actual vector resulting from the projection. In this case you want to combine it with another vector, so you need the vector version. The correct reflection formula is thus: $$R = 2(N \cdot L)N - L$$