FTL has elements of an Elite-style game, in that you control a single starship in a world that is algorithmically and randomly generated; however, the focus is less on the universe about you, and more on the ship you command.
Much of the screen is filled with the interior of your ship, showing the locations of your crew members and major ship systems and their status -- along with such things as enemy boarding parties, fires, and the like. The HUD, too, mainly reports on the status of your ship, showing damage, which systems are powered, whether a particular weapon system has been recharged and can fire again, and so on.
You are supposedly fleeing a rebel fleet; when done at a star system, and after your warp drives have recharged, you can bring up a star map and warp to one of several nearby stars. Each newly visited star provides an encounter; you may have to fight pirates or rebel craft, assist a vessel in distress, and so on. Successful actions provide "scrap", which can be used to upgrade your ship; sometimes, too, you can acquire a new crewmember, or new systems for your ship. Eventually, the "rebel front" will appear on your starmap, at which point it is time to head for the sector exit star, which takes you to the the next sector. There are nine in total, of increasing toughness, with a final boss battle series in the ninth.