The Prime Material Plane is not the only plane that exists - other planes of existence, primarily accessible by magic, form a complicated orbit around the prime material plane. However, there are occasional spots of overlap between the planes, and hapless travellers may find themselves accidentally between worlds…
Despite the name, the Ethereal Plane is not actually a true plane at all, but a reflection of the central three. Some have called the Ethereal Plane the ‘plane of magic’, as it appears to be intimately connected to the way magic works.
Bright and full of life, the Feywild is ruled by the mysterious archfey - though ‘ruled’ is a strong term for their anarchic oversight. Home to Eladrin, goblins and many strange creatures, the Feywild’s chaos and vitality can drive the unprepared to madness.
The opposite of the Feywild in many ways, the Raven Queen rules over this plane with an iron fist, sending out her agents, the mysterious Shadar-Kai. A place of death and order, it is said that if you spend too long here, your soul will wither and you will become a mere husk of yourself.
Home to the gods and their servants, the heavens and the hells are places of dream and myth more than places mortals may tread. Still, their presence is felt through the planar system in the influence of the gods and the presence of their emissaries, the angels and demons. Aasimar and tieflings are both known to have some connection to these planes, but whether that is direct descent or some sort of mystic connection is hard to establish.
The four elemental planes of Earth, Air, Fire and Water are each home to - or possibly formed of - an elemental sleeper, a great primordial creature locked in eternal slumber. Each of these sleepers reach out to the residents of their planes in dreams. Because the sleepers in Earth, Fire and Water are all broadly hostile to the Prime Material plane, this has made relations with the genasi native to those planes difficult, though the sleeper of air is more friendly, and the prime material plane has tenuous diplomatic links with the Elemental Plane of Air.
Technically speaking, the Astral Sea isn't a plane, but rather the stuff that comes between and around the planes. One notable interplanar explorer described it as 'the broth in which the soup of the planes hangs suspended', which feels like a particularly apt metaphor: the few people who have successfully completed and returned from a trip to the Astral Sea have described it as an endless flat plain of what looks like silvery liquid, broken only by mists. However, those who return from the Astral Sea tend to do so in a state of mind far from sound, so their accounts are not necessarily to be trusted.
Magical research suggests that the Astral Sea is where the souls of living creatures go when they die (assuming that they are not trapped in some other way, of course). Those brought back from death by positive necromantic magics generally describe the place they were before as being 'empty', 'dark' and 'full of stars' and tracking have suggested that they are removed from the plane. Many conjecture from this that the Sea is therefore where new souls come from as well, though the evidence for this is less complete.