Looper manages tasks that a Thread will run. It puts them in a queue and then the Thread takes the next task in line. A Looper is tied to a specific Thread.
Executor encapsulates managing and distributing tasks to different Threads. If you have a fixed threadpool size of 1 then I suppose it would be similar in design to a Looper because it will just queue up the work for that one Thread. If you have a threadpool with size > 1 then it will manage giving the task to the next Thread available to do the work, or in other words it will distribute tasks among all threads.
edit: Recommended reading: http://developer.android.com/reference/java/util/concurrent/package-summary.html
Executors are more flexible. For Android, the only time I really use Looper is when trying to make a Handler to communicate with the main thread from a background thread (which could even be in an ExecutorService). For example:
Handler mainThreadHandler = new Handler(Looper.getMainLooper()); mainThreadHandler.post(new Runnable...); //runs on main thread