Think of a hash as a much more complicated sum of digits:
1337 --> 14
I now can easily verify that 1+3+3+7 = 14
However, I can NOT say if this 14 is derived from 95, 1733, 842, 7700000 or any other number that happens to have a sum of digits equaling 14.
Adding to this, an important property of secure hashes is that it's very difficult (nearly impossible) to derive the data that produced the hash from the hash (or to find other data that produces the same hash...a collision). In this simple example it is trivial to find sets of numbers that sum to 14. Also, due to the high improbability of finding a collision, one can use a hash to verify content (i.e. if you ask someone for the data corresponding with hash "14", and they delivered 1337, you can be confident that 1337 is in fact the correct data...of course, with this trivial example, you can't because collisions are plentiful...so you can't really be sure in this example that 1337 is the correct data or if it's really 95 or 1733 or something else that would sum up to 14).