What does the "new campaign" button do in Starcraft 2?

Starting a new campaign does not erase achievements, unlocked portraits, or decals.

All it does is start the missions over, from the beginning, so you can, for instance, take the alternate routes on the 3 "choice" missions (and see the after-mission movies, which you aren't privy to when simply replaying the mission via the archive).

It may also be the only way to lower your elapsed time for the "Hurry Up it's Raid Night" achievement. (On account of being able to skip some missions)