From wikipedia: 

In discussion of the type system of a programming language, an operator from types to types is covariant if it preserves the ordering, ≤, of types, which orders types from more specific ones to more generic ones; it is contravariant if it reverses this ordering. If neither of these apply, the operator is invariant. These terms come from category theory.

In software-engineering terms, this distinction is important in considering argument and return types of methods in class hierarchies. In object-oriented languages such as C++, if class B is a subtype of class A, then all member functions of B must return the same or narrower set of types as A; the return type is said to be covariant. On the other hand, the member functions of B must take the same or broader set of arguments compared with the member functions of A; the argument type is said to be contravariant. The problem for instances of B is how to be perfectly substitutable for instances of A. The only way to guarantee type safety and substitutability is to be equally or more liberal than A on inputs, and to be equally or more strict than A on outputs. Note that not all programmming languages guarantee both properties in every context, and that some are unnecessarily strict; they are said not to support covariance or contravariance in a given context; the behaviour of some programming languages is discussed below.