The Temple trains, upgrades and improves Force Users.
The Mech Factory trains, upgrades and improves Mechs. The Shipyard trains and upgrades Ships and Submarines. The Troop Center trains, upgrades and improves Troopers. The Animal Nursery can train beasts for some Civilizations. The Power Core provides power to Buildings.
The Command Center trains the two most basic Units. To see which civilization can train which Units, refer to each individual civilization's Technology Tree. Keep in mind that unless All Techs is chosen for a game, not all Units are available to all civilizations. The Units listed here are available in any regular game.