The hanger is where players will store their transport and air combat ships, such as the Intercepter and Skyranger. Firaxis has plans to expand XCOM's air combat gameplay, but the team isn't ready to talk about these sequences at this time.
Mission Control is where you'll survey alien activity as it happens across the globe. You'll also be able dispatch your Intercepters to engage UFOs or send out field units to investigate downed alien vessels.
The Situation Room is your hard line to the funding council. The funding council is a collection of 16 countries that helped found XCOM. While you manage XCOM's resources, you are dependent on the Founding Council for a paycheck. For example, if China feels that too much alien activity is occurring within its borders, it will likely ask you to investigate. If you complete these missions, you will be rewarded. However, if you fail to keep a country happy it might permanently withdraw its support from XCOM.
The Armory is where you will view the loadouts for all your soldiers. You can equip weapons, items, armor, etc, as well as promote your units and even customize their physical features. Think of the Armory as a sub-menu to the Barracks, featuring more detailed information on specific units.
The Barracks isn't merely where all your XCOM officers live; it's also where you hire new soldiers and view their status. All of your soldiers start out as rookies. Green soldiers begin the game a little more timid in combat than veterans, but as they level up they'll grow more accustomed to firefights, become less susceptible to fear attacks, and be less likely to panic and injure themselves or their teammates.
Here you can build new armors, weapons, or equipment. You'll research new weapons and technology in the Science Labs, but the construction and implementation happens in Engineering. You will have to construct each item individually, so each commando on your team could have their own loadout.
Science Labs are where your research happens. While on the field, you collect artifacts from the aliens you kill - as well as their scientifically valuable corpses. Once you return these artifacts to the HQ, your science teams will work to reverse engineer the alien tech and construct new tools and gear for your field team. XCOM's tech tree will have some significantly divergent branches, so you likely won't be able to build everything in a single playthrough.
Soldiers who aren't killed in action might injure themselves in combat. These units will need to spend some time in the Infirmary once you get back to HQ. This provides a good opportunity to cycle new units into the fold next time you head into battle.
The Foundry lets you begin work on big technology projects such as the Super Heavy Infantry Vehicle. These units will be expensive, but they can tip a skirmish in your favor. The first type of SHIV you can build, for example, is a tank-like unit that absorbs massive amounts of damage and doubles as mobile cover for your other units. However, like the rest of your infantry, once your SHIV is destroyed, it's gone. You'll have to invest more resources to build a new unit.
As Laboratories do for Science Labs, Workshops boost the efficiency of your Engineering department. For every Workshop you build you will receive a random resource rebate on whatever you built. Recollecting resources like this will be very critical late in the game as resources become scarce. Your value of return builds as you construct workshops that are close together, so the layout of your HQ will actually have an effect on gameplay.
Much like the relationship between Workshops and Engineering, Laboratories boost the output of your science labs. As in the original X-COM, you'll be able to buy more scientists to increase the speed of your research, but building additional Laboratories will also provide a much-needed boost to your scientific advances.
Officer Training School
The Officer Training School is where you will be able to spend resources to unlock XCOM bonuses such as perks that give your soldiers a global morale boost in combat. Think of these bonus perks as the equivalent to Civilization's Wonders of the World.
Thermal Power Station
As you build your base and dig further into the Earth's crust, you'll come across pockets of steam. This steam can be harvested and used to power your base. Power stations can be built on any square, but Thermal Stations - which harvest steam - can only be built on steam squares and will significantly reduce your power bill.