The first form if-if-if tests all conditions, whereas the second if-elif-else tests only as many as needed: if it finds one condition that is True, it stops and doesn't evaluate the rest. In other words: if-elif-else is used when the conditions are mutually exclusive.
Let's write an example. if you want to determine the greatest value between three numbers, we could test to see if one is greater or equal than the others until we find the maximum value - but once that value is found, there is no need to test the others:
greatest = None
if a >= b and a >= c:
greatest = a
elif b >= a and b >= c:
greatest = b
else:
greatest = c
print greatest
Alternatively, we could assume one initial value to be the greatest, and test each of the other values in turn to see if the assumption holds true, updating the assumed value as needed:
greatest = None
if a > greatest:
greatest = a
if b > greatest:
greatest = b
if c > greatest:
greatest = c
print greatest
As you can see, both if-if-if and if-elif-else are useful, depending on what you need to do. In particular, the second of my examples is more useful, because it'd be easy to put the conditional inside a loop - so it doesn't matter how many numbers we have, whereas in the first example we'd need to write many conditions by hand for each additional number.
