A hash collision is any pair of values (preimages) that when hashed produce the same digest (image). Finding even one example of a collision should be infeasible in a cryptographically secure hash function. This is called collision-resistance. It is necessary but not sufficient for security (the hash function should also possess the property of pre-image resistance).
MD5 is an example of a hash function initially thought to be collision resistant but recently found to have collisions.