I was told my wires aren't "grounded". What does that mean?

[Kolesar]

10. Metal lamps on a circuit with no safety ground can be an electrocution hazard

The risk is if the insulation gets damaged and somehow the hot conductor touches the metal shroud of the lamp. A GFCI protector would prevent that risk.

The NEC or "fire" code assumes that lamps with only two conductors can be safely used in a room where the occupants cannot be connected to ground. The code assumes that somebody walking on carpet or vinyl floor will not be grounded. The code "requires" GFCI protection in rooms with water like the kitchen or bath and rooms with a concrete floor.

GFCI in any room is not a bad idea. One can protect the occupants by replacing the first receptacle in the circuit with a GFCI receptacle. One can also buy a GFCI circuit breaker.