Missions are classed into several types.
Ferry - You take people or cargo from one place to another. Cargo goes in your cargo hold, people go in staterooms or cryogenic chambers. Some passengers will refuse transport via cryogenic chambers, and others will be willing to pay significantly less (though you may be able to make that up in volume as CC's are much smaller and cheaper to run that staterooms).
Bounties - Find and destroy or capture persons of (usually) ill-repute. Though, depending on who is offering the bounty, you may find yourself on the wrong side of the law
Retrieval - Find some person, commodity, or item and bring them back to the contract holder.