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!")
>>> f = "Look at me!"
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!!")
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.