One way of viewing it is that it's akin to the original neo-conservatives, who were Communists who lost faith in it. If you remember William Kristol trying to be
the anti-Trump leader, his father Irving was one of its founders (note that this is
decades before "neo-con" got its current meaning).
Lots of us are libertarians or conservatives who've lost faith in those, and are pursuing and defining a new Right that's by definition an alternative to the existing Right. Me, I was a paleoconservative.
As far as a strict definition, the best I've seen so far is former libertarian Vox Day's initial attempt, 16 points which you can find at http://voxday.blogspot.com/2016/08/what-alt-right-is.html
Note that as a matter of taxonomy, he divides it into the Alt White, such as the Daily Stormer types and a group he can't belong to, and a much larger Alt West, I can dig that up for you if you want, but obviously the Alt West isn't obsessed with the Joooos, is therefore unabashedly Christian or at least believing, well, here's his 4th point:
The Alt Right believes Western civilization is the pinnacle of human achievement and supports its three foundational pillars: Christianity, the European nations, and the Graeco-Roman legacy.
The total antisemite types, I gather they don't much like Christianity because of its Jewish origins, from Jesus to the Old Testament, they're certainly fond of a lot of pagan icons.
The combativeness of point 3 is a personal characteristic of his, but is pretty essential, and you can see how Trump is aligned with it (although, frankly, if implicitly telling the press to FU is what you need to enjoy a steak dinner with your family in peace...).
Point 12 is particularly important: "The Alt Right doesn't care what you think of it.", or more simply put, "We Don't Care." Note Trump's war on Political Correctness, which alone won him more than a few votes, lots of people are utterly sick of it.
Obviously many of the points will send anyone on the left screaming, and certainly there's no universal agreement on any of this---forget it being inchoate, humans being humans there never will be!---but you can take it as being at least somewhat representative of the Alt Right.