Convert them to integers:
legs = int(raw_input("How many legs do you have? "))
arms = int(raw_input("And how many arms do you have? "))
At the moment they are strings, this is the default datatype from raw_input.
>>> example = raw_input()
2
>>> type(example)
<class 'str'>
When you add two strings together (right there you have '2' and '2'), Python just concatenates them into one single string. (So in that case it will result in '22')
>>> '2' + '2'
'22'
It should now give the correct result.
A minimal example of what the fixed version does:
>>> legs = int(raw_input())
2
>>> arms = int(raw_input())
2
>>> limbs = legs + arms
>>> limbs
4
You can now pass that to the function without trouble.