Aside from the main storyline of Crisis Core, there are 300 missions to take part in. The Mission Menu can be accessed from savepoints, and missions are sorted into categories and sub categories. You can also record your Mission Progress with the percentage in the corner of this menu.
When you open a sub category, you get a list of available missions. Each of these has a rating based from your level.
If you die in any of the missions, it's not a Game Over. Instead, you simply return to the Save Point you accessed the mission from with all your health restored. To end the mission voluntarily, simply enter the Missions section in the Menu, or by trying to cross the red dotted lines scattered about the missions.