Checkpoint
Checkpoints in Diablo 3 function something like respawn points. Players who die appear back at the last checkpoint they reached, usually at the stairs that they took to reach the current level. It's not known how checkpoints will be structured on outdoor levels.
Checkpoints are not spots on the ground that must be clicked, like waypoints were in Diablo II. They aren't visible in the game at all, until your character passes through one, at which point a "checkpoint reached" title pops with flashing graphics. There was no mechanism in the Blizzcon demo build (October 2008) to travel between checkpoints, (there were no waypoints in the build either), but the D3 Team has talked [1] about allowing players to resume a new game at the last checkpoint reached.
Convenient Travel Options
Checkpoints are meant to save players time and effort when they respawn after death, and when they start a new game. Waypoints will function much as they did in Diablo II, but instead of making the levels smaller, the D3 Team has added checkpoints into the levels, cutting down the distance players will have to retrace after they die, or when they create a new game.
In addition to waypoints and checkpoints, the D3 Team has talked about adding some mechanism (such as a town portal-like scroll) that would enable players to instantly travel from town to the location of the other players in the game. It's not clear why players in the game couldn't just cast a town portal, but it seems that those will be limited in Diablo III (as a strategic element, to prevent players from escaping back to town any time they want), so the instant location scroll is meant to save battling players any delay or pause in the action.
