If something is testable, it can be tested — you can actually check whether it is true, whether it works, or how good it is. The word is most at home in science and in computing. A scientist says an idea is testable when you could design an experiment that would show it right or wrong; an idea that no experiment could ever touch is not testable, however interesting it sounds. Programmers say code is testable when it is written in a way that lets you run automatic checks on it easily. Teachers use it too, about what can be examined. It is a formal word — you would not use it about the everyday sense of 'testing' the soup. Note the quiet judgement inside it: calling a claim 'not testable' is often a polite way of saying it is not worth arguing about, because nothing could settle it.