Entropy - The measure of randomness in a hash (In this case anyway)(Someone correct me if i'm wrong).
Basically you want a hash function to have a completely different output even if the input is only changed a tiny tiny tiny bit. So that hash of aaaaa is not even CLOSE or similar of hash of aaaab.
Collisions is when you have two different inputs that produce the same output in a hash function. There is no such thing as a hash without a collision, this is because a hash is of fixed length. However, the entropy of a hash determines "how often" a collision will occur or "how good" an hashing algorithm is.
(Someone please correct me if I am mistaken above, its getting rather late over here)