Besides what Jeremy said, its main benefit is that it has its own bit of syntactic sugar: the enhanced for-loop. If you have, say, an Iterable<String>, you can do:
for (String str : myIterable) {
...
}
Nice and easy, isn’t it? All the dirty work of creating the Iterator<String>, checking if it hasNext(), and calling str = getNext() is handled behind the scenes by the compiler.
And since most collections either implement Iterable or have a view that returns one (such as Map‘s keySet() or values()), this makes working with collections much easier.
The Iterable Javadoc gives a full list of classes that implement Iterable.