apply is designed for calling a function with a variable argument list. Conceptually, you can write any function call of the form (f a b c) as (apply f (list a b c)). Its arguments are a function, any number of arguments, and a list at the end. For instance, suppose we have (apply f x y z (list a b c)). This is the same as writing (f x y z a b c).
In your example, you have (apply + '(a b) '((c d) (e f))); apply splices in the closing list, doing the same thing as (+ '(a b) '(c d) '(e f)); it should be clear why this returns '(a b c d e f).
That was not the clearest explanation in the world, so if you still have questions, please ask.
Also, a formatting tip: indent your code with two spaces and surround it by blank lines to have it formatted as code.
