Noumena is the plural form of Noumenon, rarely used in the singular because of its particular philosophical meaning.
In the course of studying the philosophy of Immanuel Kant, one of the first hurdles of counter-intuitive thought one must overcome is his fundamental division of so-called 'noumenal' and 'phenomenal' worlds. The reason for the division is quite simple, and most integral to Kant's methodology and purpose, but first a short description the epistemological implications.
Most simply, the noumenal world is reality populated by things-in-themselves, that is, things in their actual being. Perhaps you think you've encountered this world, like when you chased that alluring ice cream truck down the hot pavement, with balloon fight water streaming off your legs and evaporating in the summer sun. You're wrong. You've never encountered even the faintest wisp of the pure thing-in-itself (ding an sich), because your mind altered your perception of it before it became fully present before your consciousness! You saw/felt/tasted/smelt/loved(?) only phenomena, and you are in fact trapped in the phenomenal world.
Confused? Scared? Maybe you should be, but try to forget about that! There is a method to the madness. Kant's whole project is defined to a certain extent as attempting to save reason from itself, that is, from the empirical ravages of Hume (poor desperate Hume, did you ever hear the one about the mud puddle?) By postulating the mind's ability/tendency to form objects (rather than conform to them), Kant creates a basis for defending unprovable principles of understanding, such as, most famously, causality. This movement of the mind from passive perception to active is often called Kant's Copernican Revolution. In short, he says that it is impossible for us to perceive the raw unstructured universe of experience of the noumenal world without structuring them to fit the principles of undertstanding.
My understanding, and the conditions under which alone it can connect the determinations of things in their existence, prescribed no rule to the things themselves; these do not conform to my understanding, but my understanding would have to conform to them; they would therefore have to be given to me in advance so that these determinations could be drawn from them, but then they would not be cognized a priori. (Prolegomena to Any Future Metaphysics).
Before I get any deeper into this mire, I must conclude that noumena exist as a sort of reality 'behind' that reality which we experience. This reality is not necessarily subject to physical laws such as cause and effect, but nor is it ever accessible to us as thinking subjects. It is radically unknowable.