Let $S$ be a simplicial complex of dimension $m$. I read the following sentence from the book "Advances in nonlinear Geosciences" by F.C Motta :
filling an $n-$dimensional hole amounts to eliminating a class $[\gamma]\in H_n(S)$ by making the cycle $\gamma$ into the boundary of an $(n+1)-$chain so that $[\gamma]=\in H_n(S)$ since $0$ and $\gamma$ differ by a boundary, namely $\gamma$.
I'm not able to understand this sentence because I don't see the meaning of filling a hole and what does it mean mathematically to eliminate a class.. and how to make a cycle into a boundary..
Thank you very much for explaining this sentence..