Every 3 days you can drop one of your missions, but still get full experience as if you had completed it normally. For the most part, this is intended as a way for players to be able to complete a mission that's bugged instead of harassing the Devs (IMO), but it has several other uses.
Dropping a mission can be a very fast way to get rid of annoying missionsFor example, if you alternate your characters a lot, it can be a way to get some fast experience just before you're about to log off. You can use it to get rid of particularly annoying missions that are easy to fail and take forever to complete (like the "Protect the Henge" mission in Croatoa). You can also use it to dump a mission that is ridiculously hard to get to or find. Lastly when trying to set up a Safeguard/Mayhem (where you have to do a certain number of radio/paper missions), dropping one gets you to the Safeguard faster.
Keep in mind that you can't drop timed missions or missions that are part of a Task Force.
To drop a mission, all you need to do is talk to the contact that gave you the mission. If you have the cell number and can call, it's pretty easy. Otherwise, you'll need to run back to where they are and talk to them in person.