MSDN says:
A hash code is a numeric value that is used to identify an object during equality testing. It can also serve as an index for an object in a collection.
The GetHashCode method is suitable for use in hashing algorithms and data structures such as a hash table.
The default implementation of the GetHashCode method does not guarantee unique return values for different objects. Furthermore, the .NET Framework does not guarantee the default implementation of the GetHashCode method, and the value it returns will be the same between different versions of the .NET Framework. Consequently, the default implementation of this method must not be used as a unique object identifier for hashing purposes.
The GetHashCode method can be overridden by a derived type. Value types must override this method to provide a hash function that is appropriate for that type and to provide a useful distribution in a hash table. For uniqueness, the hash code must be based on the value of an instance field or property instead of a static field or property.
Objects used as a key in a Hashtable object must also override the GetHashCode method because those objects must generate their own hash code. If an object used as a key does not provide a useful implementation of GetHashCode, you can specify a hash code provider when the Hashtable object is constructed. Prior to the .NET Framework version 2.0, the hash code provider was based on the System.Collections.IHashCodeProvider interface. Starting with version 2.0, the hash code provider is based on the System.Collections.IEqualityComparer interface.
Basically, hash codes exist to make hashtables possible.
Two equal objects are guaranteed to have equal hashcodes.
Two unequal objects are not guaranteed to have unequal hashcodes (that’s called a collision).