|This is a /v/ related article, which we tolerate because it's relevant and/or popular on /tg/... or we just can't be bothered to delete it.|
The short version? They were some of the first computer roleplaying games to get popular. Ultimas 1, 2, and particularly 3 were old school hack & slash affairs, with brief voyages into Science Fantasy just to liven things up.
After receiving feedback from his first 3 games, Richard Garriot (author of Ultimas 1 through 3) decided to make a game about virtues and ideals that are beyond just killing shit (perhaps inspired by the fact that one of the more viable strategies in 3 was to wipe out an entire peaceful town... repeatedly). The result was probably one of the most influential Western computer RPGs ever made: Ultima 4: Quest of the Avatar. (Fun fact: the word "Avatar" for an in-game character starts with Ultima 4.) What was unique about it? It had a plot that was more than an excuse for dungeon crawling or combat; the basic idea was to become worthy of being a champion of the realm of Britannia.
And he followed it up with 4 sequels that attempted to top it, along with some spinoffs that go in some different directions with innovations of their own. Ultima Underworld, for example, was one of the earliest first-person RPGs to have a real 3D engine. Ultima V: Warriors of Destiny had a day/night cycle, and NPCs that would move around following a schedule — a cunning player could trail one and learn all manner of secrets, such as secret meetings of a resistance movement, or where treasures had been hidden.
One characteristic the early Ultima titles had was a genuine attempt at immersion, through inclusion of physical props boxed in with the game. These included cloth maps, amulets and coins.
And then EA came. We don't speak about that, mainly because it's a story that's being told all too often — company gets bought out, company's games decline in quality, company is shuttered and the IP gets shelved until the end of time or until they need another shooter.
But we will speak about how the first western MMORPG — if you ignore MUDs — was Ultima Online, a game so influential to the point that it coined the word "MMORPG".
If you want more detail, go look for The Spoony One's review of the series. The guy is an idiot, but he gives a good overview of what the series was like, and why Ultima 9 is so hated. If it's still up when you read this, here's a version that cuts out the skits. You could also look at HardcoreGaming101's retrospective on the entire series, which includes all the spinoffs.