In the year 1998, the amount of reports of UFO sightings has been drastically increased. Stories about abductions and alien attacks became more and more widespread. Finally, after various nations of the world have failed to intercept the UFOs, their representatives met in a conference of global importance in Geneva, Switzerland. It was eventually decided to organize a secret paramilitary group, dubbed Extraterrestrial Combat Unit (X-COM). Starting with one base, two fighters, one transport, and a few soldiers, X-COM must locate the aliens, learn about their origins and technology, find out where their base is, and destroy it.
X-COM: UFO Defense is a strategy game featuring separate but interlinked elements. On the strategic side, called GeoScape, you get a rotating view of the globe, where you see all visible UFOs (those that are within your detection range) as well as major cities and your base(s). You order movements from here, such as sending out fighters to intercept UFOs, transports with soldiers to assault/recover UFOs, and perhaps assaults on alien bases (if you find any). You also control your research, as you must invent better weapons (the Terran weapons are just no match against the alien weapons) quickly, not to mention all the other cool tech you can recover from the aliens. You also need to control your budget, as you can't afford to overextend your reach. Researchers need to be paid, engineers (who build the new toys) need to be paid, base(s) need to be be built/expanded, planes need to be bought/maintained, supplies need to be replenished, and so on.
You can earn money by selling unneeded stuff, and you receive funding from the nations of the world; however, a nation can decrease its funding if it decides you aren't operating efficiently enough within its region. It's even possible that a nation gets so fed up with you that it signs a pact with the aliens and ceases funding altogether.
Once you join a ground battle, the game switches to Battlescape, which is an isometric view of the battlefield with realistic line-of-sight calculations and turn-based combat. Your mission is usually extermination of all aliens on the battlefield, though if you can capture a few it would surely help your research efforts. If you win, you also recover any alien artifacts left on the field, which can then be researched.
In combat, each of your soldiers has a specific number of Time Units. Doing anything (moving, shooting, turning around, rearranging objects in the inventory etc.) costs a number of TUs. Once a soldier is out of TUs, he cannot act any more this turn (he gets all his TUs back on the next turn, though).