It means that the dot product satisfies two properties:
* If $u$, $v$ and $w$ are vectors such that $\cdot$ and $+$ make sense, $$u \cdot (v + w) = u \cdot v + u \cdot w$$ and vice-versa: $$(u + v) \cdot w = u \cdot w + v \cdot w$$
* If $u$ and $v$ are vectors such that $\cdot$ makes sense, and $c$ is a scalar, $$(cu) \cdot v = c (u \cdot v)$$ and vice-versa: $$u \cdot (cv) = c (u \cdot v)$$