Listening to the Collections lecture from Functional Programming Principles in Scala, I saw this example:
scala> val s = \"Hello World\"
scala> s.flat
With map you are taking a list of characters and turning it into a list of strings. That's the result you see. A map never changes the length of a list – the list of strings has as many elements as the original string has characters.
With flatMap you are taking a list of characters and turning it into a list of strings and then you mush those strings together into a single string again. flatMap is useful when you want to turn one element in a list into multiple elements, without creating a list of lists. (This of course also means that the resulting list can have any length, including 0 – this is not possible with map unless you start out with the empty list.)