Why can any closed manifold be constructed a fundamental class of coefficient $\mathbb{Z/2Z}$?

Question

I am reading now a Milnor and Stasheff's "Characteristic Classes". In the page 274, there is a sentence "The case $\Lambda= \mathbb{Z/2}$ is particularly important, since the mod 2 homology class

$\mu_{K} \in H_{n}(M, M\setminus K;\mathbb{Z/2}) $

can be constructed directly for an arbitrary manifold, without making any assumption of orientability." which I cannot understand. Are all manifolds $\mathbb{Z/2Z}$ orientable? And if it's true, why?