What are the colored plastic strips that came with my flash, and how do you use them?

They’re flash gels: thin colored filters that go over the flash head to change the color of the light.

Main uses:

• match ambient light so flash blends naturally
• create a deliberate color effect

Common correction gels:

• cto (orange): warms flash to better match tungsten/incandescent light or give a sunset-like warmth
• ctb (blue): cools the flash to match cooler light sources or for a cooler look
• ctg / green: helps match fluorescent-type lighting

Creative use:

• use colored gels on a flash aimed at a wall or background to make the background glow with color
• combine gels for different effects
• use flags or blockers to keep the colored light off your subject if you only want the background colored

In short, they either help your flash match the scene’s existing light, or they let you stylize the light for effect.