After liberating an Outpost and accessing new Radio Towers, these will become available to you via random locations on the map. The Supply Drop quests are shown to you via a Blue Plus icon. These quests are a checkpoint race, where you need to deliver the medic kit to a set location.
At the start, you'll be given a vehicle and then you'll need to drive and follow the smoke checkpoints to the destination. You'll want to get there as fast as possible as you're also given a time limit. Most of these are pretty easy to finish on time, but some are a little harder due to the terrain you have to cover. Just take each part carefully and don't put your foot down in hilly or bumpy areas.