When you are talking about of an relation, you gotta to think that this is inter two given sets. So a relation R inter set A and a set B is a subset of their cartesian product:

An equivalence relation in a set A is a reation i.e. a endo-relation in a set, which obeys the conditions:

• reflexivity
• symmetry
• transitivity

An example is used when we use sum of fractional numbers. Here a rational number can be represented of several different fractions, so by taking the fractions having a common denominator we can simplify the result.