A hash is an fixed sized integer that identifies a particular value. Each value needs to have its own hash, so for the same value you will get the same hash even if it's not the same object.
>>> hash("Look at me!")
4343814758193556824
>>> f = "Look at me!"
>>> hash(f)
4343814758193556824
Hash values need to be created in such a way that the resulting values are evenly distributed to reduce the number of hash collisions you get. Hash collisions are when two different values have the same hash. Therefore, relatively small changes often result in very different hashes.
>>> hash("Look at me!!")
6941904779894686356
These numbers are very useful, as they enable quick look-up of values in a large collection of values. Two examples of their use are Python's set and dict. In a list, if you want to check if a value is in the list, with if x in values:, Python needs to go through the whole list and compare x with each value in the list values. This can take a long time for a long list. In a set, Python keeps track of each hash, and when you type if x in values:, Python will get the hash-value for x, look that up in an internal structure and then only compare x with the values that have the same hash as x.
The same methodology is used for dictionary lookup. This makes lookup in set and dict very fast, while lookup in list is slow. It also means you can have non-hashable objects in a list, but not in a set or as keys in a dict. The typical example of non-hashable objects is any object that is mutable, meaning that you can change its value. If you have a mutable object it should not be hashable, as its hash then will change over its life-time, which would cause a lot of confusion, as an object could end up under the wrong hash value in a dictionary.
Note that the hash of a value only needs to be the same for one run of Python. In Python 3.3 they will in fact change for every new run of Python:
$ /opt/python33/bin/python3
Python 3.3.2 (default, Jun 17 2013, 17:49:21)
[GCC 4.6.3] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> hash("foo")
1849024199686380661
>>>
$ /opt/python33/bin/python3
Python 3.3.2 (default, Jun 17 2013, 17:49:21)
[GCC 4.6.3] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> hash("foo")
-7416743951976404299
This is to make is harder to guess what hash value a certain string will have, which is an important security feature for web applications etc.
Hash values should therefore not be stored permanently. If you need to use hash values in a permanent way you can take a look at the more "serious" types of hashes, cryptographic hash functions, that can be used for making verifiable checksums of files etc.
