Tristram is a recurring town in the Diablo series where many important events happen. It is depicted as the usual medieval RPG town, with taverns, blacksmith, etc.
The story revolving around Tristram is an interesting one:

The story of Trinstram starts way back when the Prime Evils where banished from the Burning Hells by the Lesser Evils. During this period, the Horadim mages rallied together to trap the Prime Evils into Soulstones. When they finally captured Diablo and his brothers, they buried Diablo under a series a caverns and built a Horadric monastery to stand guard over the location.
People started to slowly move into the area surrounding the Monastery, forming the town we know as Tristram. With Diablo out of the picture, the Horadim mages slowly dwindles until they where all but forgotten. As Tristram thrived and expanded, less and less people where aware of the dark secret that buried under the monastery.

It was when Leoric conquered the Khanduras kingdom and made Tristram the capital that Diablo would slowly fade into the story again. Leoric had made the now ancient Horadrim monastery his seat of the power from where he ruled the lands. Archbishop Lazarus (Leoric's most trusted adviser) was becoming attracted by the Soulstone buried deep under the monastery. He eventually ventured into the deep levels of the cathedral, where he became corrupted by Diablo.
Diablo initially attempted to possess Leoric, but his indomitable strength was too much even for Diablo. He did however manage to drive Leoric mad. As a second choice, Diablo possessed Leoric's son, Albrecht. This time he was successful and now had a body he could use to manifest in Sanctuary. The disappearance of his son caused Leoric to become even more mad, resulting in the following:
- He sent his knights on the advice of (the now corrupted) Lazarus on a suicide mission against the bigger Wastmarch
- Killed over half of Tristram's population on counts of treason, blaming them for his son's disappearance
Leoric was eventually killed by the knight Lachdanan, but this was not the end of it for Tristram. Soon after his death, monsters started pouring out from the Monastary into Tristram. Lazarus managed to manipulate the townsfolk into finding shelter in the lower regions of the Cathedral, only to find that they where trapped in a room with The Butcher. He killed many of them, and the few survivors either left town or tried to survive the demons.
It was a lone hero (the player, of course) that eventually saved Tristram. He ventured into the Cathedral killing Lazarus, the Skeleton King (the now corrupted Leoric), and The Butcher. He then ventured into hell to kill Diablo himself, which he did. However, by the time he killed him the hero had become corrupted by Diablo's influence, causing him to think that the only way to fully contain Diablo is to insert his Soulstone in his forehead.
The Soulstone eventually corrupted the hero making him the Dark Wanderer. As he emerged from Hell, the hero destroyed all of Tristram and it's inhabitants, except for Deckard Cain. He then set course to free his brothers, Baal and Mephisto.

A new band of heroes (again, this is you the player) was formed to stop the Dark Wanderer and kill his brothers.
Merchants seeking to make money off of adventurers going into the Cathedral formed a "town" which later became known as new Tristram. The town slowly went into decline however when the Cathedral had been fully looted.
In Diablo 3, Deckard Cain returned to Tristram's Cathedral to study what is happening with the angels and demons. However before he could warn the people of the impending danger, a huge meteor hit the Cathedral, the original place where Diablo invaded Sanctuary.