I get into fantasy settings to get into the lore and stories of it.

And Dungeons and Dragons for me is by far the most mysterious, I know Tolkien lore, Warhammer lore, Warcraft lore, a bit of Elder Scrolls, but nothing on Dungeons and Dragons.

So what is this world or in this case Worlds since there are a bunch of campaign settings lets start with the official mainstream one, the Forgotten Realms.

Yeaaaaaaaaaaaaah.Really?

Up to and including AD&D 2nd, there was some sense in D&D worlds.
After that, they really aren't self-contained or in any way consistent or believable.

Just pure high fantasy and, as soon as you start looking for some foundations... well, there is none.

But that's me.

I don't know what the common practice is, but every group I played D&D with always just used it as a ruleset for a homebrew setting. At most we used some official map, but I can't think of any instance of some "D&D lore" factoring into the campaign.

By far the best D&D lore has been authored by a certain Jack Thomas Chick, but I'm not certain that's what you're after.

Here's a brief timeline for the part of Toril (or Abeir-Toril) that is known as Forgotten Realms.

You are asking for something similar to "What's the lore of Europe" btw.

At the time I was playing (mid 90's) there was about 10 different realms, each with its own history and back story.

They also added Planescape, which was a realm connected to all other realms.

None of them contained the Dungeon and Dragons ride from the 80's TV series

Why don't you have a look at Dragonlance, too? You may like it more.

http://dragonlance.wikia.com/wiki/Dragonlance_timeline

R. A. Salvatore has at least some claim to that.
I personally prefer Weiss and Hickman.

Greyhawk is my hands down favorite setting. It's the one used on my favorite NWN PW server and the one we used in our PnP D&D games. I don't mind the Forgotten Realms setting, but don't care enough about it to delve deeply into the lore. I just tend(ed) to pick up bits and pieces when I play(ed) FR-based CRPGs or when I read the basic rule books.

Actually that may be a good place to start. Just grab the latest iteration of the D&D rule books and read those. If you're looking for more detail, there are tons of books and on-line resources as well. Google would likely fix you right up.

Lore of Dungeons and Dragons, at least post Baldur's Gate "enhancements" and especially Siege of Fa, i mean Dragonspear, is pretty much a redundant SJW manifesto and the twisted mazes of disturbed writers' minds (to be precise, failed former D&D campaign writers'), such as Amber Scott's (The, tm).

What about characters?

Who are the Aragorns and Morgoths and Zeus' in this world or at least in the Forgotten Realms campaign setting?

Who are the main human factions for instance?

For which time period? The Forgotten Realms timeline is ~36000 years, with stuff happening all the time. So you do have a ton of people that played a big part. The Heroes' Lorebook supplement for AD&D 2nd Edition lists 60 Heroes while the Villains' Lorebook lists 29 characters, 17 creatures and monsters and 9 organizations. And considering those books were printed in 1996 and 1998, they are certainly missing a ton of other characters.
Saying that the important characters in Forgotten Realms are more than the number of names in the Silmarillion may not be far off.

Maybe start with your favorites?? Or maybe your nemesis! Nemeses? :-D

I know it has some developed settings, but I thought the point of D&D was to make up your own stuff? :p