Observables are simply the objects in an observer pattern. Wikipedia defines it succinctly.

The observer pattern is a software design pattern in which an object, called the subject, maintains a list of its dependents, called observers, and notifies them automatically of any state changes, usually by calling one of their methods.

The simplest analogy of an observer pattern can be given using a DOM event. Let's say you have a DOM element <button> with "button" as its id attribute; and consider the following code:

var button = document.findElementById("button");
button.addEventListener("click", myAwesomeClickHandlerFunction);

If you call the <button> node, a subject (or an observable); the event listener "click" on the <button> node is analogous to an observer; and myAwesomeClickHandlerFunction, its method.

You can read this article and study the (JS) code within, for a yet better, and deeper understanding of the observer pattern. The CycleJS, RxJS pages that you have come across are, I believe, documentation for the RxJS implementation of observables / observer pattern (apparently there's RxJS underneath Cycle.js).

I use observables with knockout.js.

An observable is an object, array or property that triggers a change event.

You can subscribe to this event and do what ever you want to do with that information (for example: validate values, update the DOM, trigger an API-request, ...).