1.
def fib(n):
    """ Calculates the nth Fibonacci number recursively """
    if n == 1 or n == 2:
        return 1
    else:
        return fib(n-1) + fib(n-2)

2. The problem is that you're doing a lot of repeated work by calculating
it from the top down.  If you look at all of the function calls:

fib(n)
  fib(n-1)
    fib(n-2)
      fib(n-3)
        ...
      fib(n-4)
        ...
    fib(n-3)
      fib(n-4)
        ...
      fib(n-5)
        ...
  fib(n-2)
    fib(n-3)
      ...
    fib(n-4)
      ...

At each level, we see that we're recalcating values over and over again. 
For example, 

- fib(n) calls fib(n-1) and fib(n-2)
- fib(n-1) calls fib(n-2) and fib(n-3)

We'll calculate fib(n-2) two times.  As we continue on further, we'll
see even more repitition.