An Alternate Universe is a plot device to create "what if" scenarios. They are also used to narrate other sides of a character that may not be possible in the main story arc.
An alternate universe is also referred as an alternate time-line, or alternate future. The alternate futures are possible futures which could happen depending on the actions of the past. However, these futures may actually be separate universes in a what-if scenario.
The Age of Apocalypse is an example of an alternate universe where Professor Xavier was accidentally killed by his own son, Legion when he went back in time to kill Magneto. As a result, Apocalypse ruled this altered timeline in which Xavier had never founded the X-Men.
Alternate Universes are generally very short lived and often created to demonstrate a 'what if' scenario. The Marvel What If? volumes as well as the Marvel Zombies are a good example of this. The comics describing the alternate universes are usually short, and after they are narrated, they disappear.
Alternate universe was also shown on the TV series called Sliders where the four sliders travel to each parallel Earth. These parallel Earths have their own alternate histories which would lead to the present day changes. However, the time travel wasn't involved in creating these alternate universes.
A Parallel Universe is more of a static. An example of this may be an 'opposite' universe, in which the good guys are the bad guys, and the bad guys the good guys. Parallel Universes may be described in mini-arcs, or they may only exist in another Alternate Universe.
Leading up to the year 2000 Chaos! Comics devised a 2 year story arc for all its characters where by all the story-lines of the main characters converged around a single story thread that culminated int he total destruction of their universe. In the year 2000 the Chaos Comics universe was remade by a single character who devised 8 worlds and placed each of the main characters into these worlds, reborn for their stories to continue afresh.