When an alien Foreman deploys a base, the Extractor is the first-priority structure to be built, along with a Reactor. When an Extractor is deployed, a Harvester (or, in Reaper-17's case, a Shielded harvester) will come out to automatically harvest nearby Tiberium fields. When the Harvester is full or the Tiberium field is depleted, it returns to the Extractor. As the Tiberium is delivered to the Extractor, funds are made available to the Foreman.
The Extractor seems to refine the harvested resources into some kind of energy, this is supported by the fact that the Scrin do not need a structure for Tiberium storage and can instead store an unlimited amount of resources. GDI and Nod, on the other hand, have to build Tiberium silos. However, if the aforementioned factions are able to capture at least one Extractor, they will have the ability to store infinite Tiberium, interestingly.
Sometimes, harvesters can erroneously dock at the Extractor at a section other than the one they are supposed to.