When you're in a relationship, you're emotionally involved or at least connected in some way. If you're related to somebody — your parents, your aunts and uncles, your cousins — you share a family relationship with them.
You can also use relationship to describe dealings between various groups, as “Members of the European Union have a relationship of economic interconnectedness,” or “A lease helps define your relationship with your landlord.” You'll also see relationship used with interactions that don't directly involve people. In many of these cases, the word relation is better. For example, in the sentence "We are always looking at the relationship between ticket price and sales," it would be better to use relation.