You can try the following in a interactive shell:
>>> assert 5 > 2
>>> assert 2 > 5
Traceback (most recent call last):
File "<string>", line 1, in <fragment>
The first statement does nothing, while the second raises an exception. This is the first hint: asserts are useful to check conditions that should be true in a given position of your code (usually, the beginning (preconditions) and the end of a function (postconditions)).
Asserts are actually highly tied to programming by contract, which is a very useful engineering practice