When definig the tensor product, the textbook says that:
The tensor product $M \otimes_RN$ is constructed as the quotient of the free module $R^{\oplus(M\times N)}$ modulo the submodule generated by the following elements, where $(m,n)$ stands for the standard basis element $e_{(m,n)}$: $$(m+m',n) - (m,n) - (m',n)$$ $$(m, n+m') - (m,n) - (m,n')$$ $$(xm,n) - x(m,n)$$ $$(m,xn) - x(m,n)$$ for all $m,m'\in M$ and $n,n' \in N$ and $x\in R$.
The problem is that I do not really understand which or how are those elements and how do I need to understand the quotient. Can somebody give an explanation of how these quotient and elements work?