Hash collision is a condition in which a hash function gives the same hash code or hash table location for two different keys.
In practice, this would mean that there might be, for example, two passwords that encrypt to same value - thus there are two passwords that can be used to enter the system.
A more practical example: Suppose you have a lot of forms from different people and you want to sort them to piles by the first letter of their surname. If there are many people that have names that start with same letter (probability approximately 1/26), there will be more than one paper in those piles. Then, your "hashing system" would need to cope with this hash collision, probaby by sorting the piles again by the second letter of the surname: Again there's a 1/26 possibility that there's more than one with same second letter... Now you have 26*26=676 piles labeled 'aa', 'ab' and so on, but at least you get low piles!
For some hash functions, like MD5, hash collisions are extremely unlikely, but nevertheless they do occurr. This is because of the nature of hashing (the idea is to find a short representation for arbitrary-length data).
See: Birthday Paradox
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