You can naturally extend the intuition of a functor to Applicative, and from there to a monad.
An explanation might go as follows:
Let's say I have a list of numbers and want to add 2 to each. I'd
write fmap (+2) [1..10]. But what if I had two lists of numbers and
wanted to add each number from the first to each number from the second?
Well, with Applicative, you can do that - it's like fmap, but with
multiple arguments. You just write (+) <$> [1..10] <*> [11..20].