Well First off. X-com is like the basis for Resource management and Turn based games.
Heres a video to watch while I explain the awesome factor
http://www.youtube.com/watch?v=OqrBWjiNyjYKeep in mind the game is pretty old now so don't expect Uber graphics.
The game starts with a representation of the globe. You get to place your base on any land area in the world. You'll want to consider the nations/Continents around your base area because Initially you only have basic Radar which will only detect UFO's in a relatively small area.
You place and Name the base.
The base starts with 2 Interceptors(for shooting down UFO's) and a transport(for getting your operators to the crash site.
Basically you will detect and Engage UFO's, then you'll land troops at the crash site and eliminate all the Aliens. When you win a mission you recover tech and Corpses. These items are taken back to your base where you manage your Scientists and the projects they will research. Once you've researched something you can manufacture it with Engineers.
You manage the money that Governments/Continents pay you for defending them(thats your monthly budget-Do poorly and governments will cut funding or pull out entirely)
You will expand the facilities in your base to allow you better manufacturing, or more research or storage of live aliens. Eventually you will have multiple bases around the world and some really top notch aircraft to shootdown big UFO's and some really cool tech from Plasma weapons to Psi weapons.
You win the game by going to the Alien world and killing them.