There is no such thing as a "spiritual," "mental," or "emotional" plane. The planes, if you believe in them, are about the multiple "layers" of existence in which different beings live. There is one less-common reference to planes that you may hear of in certain astral projection books, being referred to as an "astral plane" and an "ethereal plane," where "ethereal" is where they say you're going if you stay in your own world (for example, to visit someone who you can't see physically right now to check and make sure they're okay, or to look at tourist attractions in Italy for fun), and the "astral plane," according to these books, would be when you are leaving Earth entirely into another realm. However, this type of definition is very uncommon, and moat people would refer to either as the astral plane, or to Earth by using no special words and to anything else you see while projecting as the astral plane.
The MUCH more accepted idea of what planes are, is based basically on what "layer of existence" various beings live. For example, one plane may mainly be inhabited by demons, and one will he mainly inhabited by spirits (known to non-Pagans as "ghosts"). Still another may be inhabited by gods or by a certain pantheon, another may be various kinds of brownies, etc. One semi-common belief is in the 7 Planes of Existence, the very highest of which is the Asatrau, however, these 7 planes referred to in that idea are all various levels of the astral plane, with the 7th being the one farthest away from human existence. The people who believe in the 7 planes will still note the existence of the different levels of vibration for other inhabitants of space (the reason humans cannot generally sense these things is due to different levels (speeds) of vibration). As humans, most of us can only sense the physical during our daily lives, and completely ignore or even purposefully blind ourselves to anything else that may be going on around us. The first step in exploring any plane is to open your mind to be able to see or sense the things that are not mundane.