Quiz: Remember the definition of mal de mer?
The generalisation of pattern matching that is the logic programming equivalent of instantiation in logic. When two terms are to be unified, they are compared. If they are both constants then the result of unification is success if they are equal else failure. If one is a variable then it is bound to the other, which may be any term (which satisfies an "occurs check"), and the unification succeeds. If both terms are structures then each pair of sub-terms is unified recursively and the unification succeeds if all the sub-terms unify.
The result of unification is either failure or success with a set of variable bindings, known as a "unifier". There may be many such unifiers for any pair of terms but there will be at most one "most general unifier", other unifiers simply add extra bindings for sub-terms which are variables in the original terms.