A relation $R$ on a set $A$ is any subset of $A\times A$, i.e. any set of ordered pairs $(x,y)$ such that both $x$ and $y$ belong to $A$. Often we write $x\mathrel R y$ instead of $(x,y)\in R$. Typical examples are partial orders, e.g. the relation $\le$ on $\mathbb N$ and equivalence relation, e.g. the relation $=$ on $\mathbb N$.
This tag is intended for questions concerning partial orders, equivalence relations, properties of relations (transitive, symmetric,...), composition of relations and similar stuff. More-or-less the things about relations taught in the first elementary set theory or discrete math course.
For more information see e.g. Wikipedia article.