The Planetside 2 wiki page has a great key for all of the icons here. This information comes from that site.

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Generators

Any non-Max infantry can overload any generator. Doing so alerts the defending faction, however, and they can stabilize and/or repair the generators. It is usually prudent to keep these points guarded.

Vehicle Shield Generators

Vehicle shield generators block attacking vehicles from entering a facility. They also block shots from vehicles and turrets, but infantry can shoot and pass through it.

Horizontal and Vertical Shield Generators

These shield generators are paired together, so both must be controlled to control the base. They occasionally protect security terminals (see below), and in such cases these shields must be disabled before moving on to capturing control points.

SCU Shield Generators

These can be found in Bio Labs and protect the SCU. Disabling this generator allows an attacking faction to penetrate into a base's Spawn Control Unit (SCU). If the SCU goes down, the defending faction cannot respawn at the facility, so this is a big priority.

Security Terminals (aka "Control Points")

Like generators, "control points" can be captured by any non-Max character, provided they are not in a vehicle. When all of the control points for a given base have been captured by a given faction, the base "flips" to the attacking team.

These control points are sometimes hidden behind shield generators, so in these cases, the shield generators need to be taken down before an attacking faction has access to the control point behind the shield.

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Terminals

Terminals allow the faction controlling them to do a variety of useful things. They can be captured by an infiltrator, and repaired by an engineer. When their facility flips, control of them flips to the new owners of the facility (I think?).

Equipment Terminals

Allows a player to change class and/or resupply.

Sunderer Terminals

Allows a player to spawn in any of the non-faction-specific ground vehicles: Flash, Sunderer, Harasser, or Lightning. They are more limited than the Vehicle Terminals (see below) because they cannot spawn the faction-specific Main Battle Tanks (Prowler, Vanguard or Magrider).

Vehicle Terminals

A vehicle terminal allows a player to spawn in any ground vehicle their faction is capable of spawning in. They are essentially like Sunderer Terminals (see above), but they additionally allow a player to spawn in one of the faction-specific Main Battle Tanks (Prowler, Vanguard or Magrider) if their faction controls a Tech Plant on that continent.

Air Terminals

Air terminals allow a player to spawn any air vehicle except the Galaxy, which has its own terminal (see next).

Galaxy Terminal

A Galaxy terminal allows a player to spawn a Galaxy, which serves as a mobile spawn point for members of the owner's squad.

Energy Bridge Terminal

Rarer than the other terminal types, these terminals control energy bridges, which can be set to faction-specific (the bridge supports only the owner's faction but other factions fall through) or neutral (bridge supports all factions).