The Buildings screen of a base is where you order the construction of additional facilities for your base. This is necessary, for example, if you want to increase your research capacity (with a lab), make more room in your storage (with additional storage modules), make space for a new craft (additional hangers), or speed up your soldiers healing process (with a hospital).
Please keep in mind that there are three "elementary" buildings needed in each base before the base is functional at all. These are: an Entrance (pre-built for each new base), a Power Plant and the Command Center.
New bases can be built using the world-map, so you don't need to place all non-vital facilities in one site. Doing so would be problematic, as space is limited.
See also the list of Base Facilities.
Get more information on a building
When placing a building a "building preview" is displayed. This lists the cost to build, monthly upkeep costs, other buildings required, and the number of identical buildings already built in the base.
Before you finally place a new building make sure you have read its complete UFOpaedia entry. There you can find out what its purpose is, and other details. You can access this entry through the UFOpaedia itself, or by pressing the small magnifying glass icon in the building preview .
Another important aspect to take into account when expanding your base is building time. Buildings vary greatly in the amount of time needed to be built, some up to 2 weeks.