Manifolds as homology classes

Question

I have found that a k-dimensional submanifold of a manifold M can be considered as a class in the homology group $H_{k}(M)$. Why ?

Answer 1

If $X \subset M$ is an oriented submanifold of $M$, then $X$ has a top homology class $[X] \in H_k(X)$. It gets sent, via the inclusion $i : X \to M$, to a class $i([X]) \in H_k(M)$. This is generally what is meant by considering a submanifold as a homology class; I'm not sure it makes sense for nonoriented manifolds.