One of the biggest additions in Halo: Campaign Evolved is the inclusion of three new bonus missions set two years before the events of the original Halo campaign. This mini-adventure involving Master Chief and Avery Johnson is separate to the main story, however, meaning you can either play it before or after, or even during the main story if you're an absolute savage.
The remake also adds new terminals and 32 additional skulls—collectible modifiers you can find in each mission, including the bonus missions, and use to tweak your playthrough.