The fibonacci function (2 base cases, 2 recursive calls):
fibonacci(0) = 1
fibonacci(1) = 1
fibonacci(n) = fibonacci(n-2) + fibonacci(n-1) [for n>1]
Let's compute fibonacci(4):
fibonacci(4)
=  fibonacci(3)                  + fibonacci(2)
= (fibonacci(2)  + fibonacci(1)) + (fibonacci(1) + fibonacci(0))
= ((fibonacci(1) + fibonacci(0)) + 1) + (1 + 1)
= (     1        +      1      ) + 1) + (1 + 1)
= 5

Computing Examples

Structural definition of a Stack:

For example S = (7,(29,(11,EMPTY)))

Recursive definitions are extremely common in Computer Science (e.g. Lists, Trees, etc).