After the first level, of the escape from Area 51 (Groom Lake), Agent Carter is brought to The Bureau's main base. From the Operations Room console, there are three kinds of missions accessable.
Major Operations are the main plot-driving missions, and require some activity around the base to progress. On the Mission Map, they are marked with a Sectoid head with two flags.
Minor Operations are supplemental missions, and the main source for equipment and experience for Agent Carter. Some Minor Operations need to be unlocked by performing certain tasks in the Base. They are marked by a Sectoid head with one flag.
Dispatch missions appear after each Major Operation, and some can be unlocked like Minor Operations. Agent Carter does not go out on these missions. Instead, any spare agents are sent out in their own squads, up to 5 Agents of any mix-- providing that their combined level matches or exceeds the "Mission Complexity" rating (ie: a rating of 8 can be performed by two Level 3 Agents & a Level 2, or two Level 4 or Level 5 Agents). After Agents are assigned to a dispatch mission, Carter himself must go out and complete a Major or Minor operation. When he returns, the Dispatch mission will also be completed. The rewards of such is that all sent Agents gain a level (if they have not maxed out at level 5 already), and a reward that is listed in the Mission's description. Rewards include a new mid-level agent, or a new Pack type.
List of campaign missions on the Bureau: XCOM Declassified.