Avalon is a place widely associated with Arthurian Britain, on one or more levels, depending on whom and what you read. In the most fantastical of Arthurian stories, Avalon is a magical place, where Arthur is even now residing, awaiting a call to defend his homeland again from hostile invaders. The idea is that Avalon is a resting place of sorts for souls. Celtic beliefs of Ancient Britain included the idea that the soul never died but went to such a resting place, there to await another journey in another life. Avalon, as popularly imagined, would certainly fit that bill.
One of the oldest of the tales that mention Arthur by name, The Spoils of Annwn, from The Book of Taliesin, refers to Annwn as the place the Ancient Celts called the Otherworld. In this story, Avalon is portrayed as the resting place for souls about to enter Annwn. (In the story, by the way, Arthur and a few choice friends go to Annwn to recover a cauldron. This was, perhaps, an early representation of what we now call the Grail.) So perhaps Arthur is in Avalon after all, having not descended into Annwn but instead been kept in a state of limbo, better to return and fight anew when the time is right.
Another element of the story of Avalon, as it is with many other Arthurian elements, is geography. Historians spend their lifetimes trying to find the location of places that are mentioned, in some way or other, in the Matter of Britain but have never been positively charted on a map. Such is the case with Avalon. Many a historian and many a reader of the Arthurian literature believe that Avalon was Glastonbury. Avalon was described as an island. Glastonbury was surrounded by water long ago. The town has a Tor, a large oblong-shaped hill, nearby as well, which is surrounded by apple orchards. For as long as Avalon has been mentioned, it has also been called "the Apple Isle."
No connect-the-dots evidence exists to prove that Glastonbury was Avalon or that anyplace else was Avalon. We simply don't know where it was. Perhaps, if The Spoils of Annwn are to be believed, it is a place that isn't easily accessed or is underground or otherwise hidden from our view. Perhaps, if Marion Zimmer Bradley is to be believed, Avalon has faded into the mists of history and fancy, taking Arthur along with it. (Now that would be an excellent reason why we can't find it: It isn't here anymore.)
Whatever we all believe is entirely up to us. Some clues point to a physical location, perhaps one that is with us still. Other ideas have the place not really a place in the physical sense. It is an interesting proposition, though, to continue to reconstruct the elements of the Matter of Britain, trying (mostly in vain) to succeed where so many others have come up short.