"Killing the ambient" means reducing the scene’s existing light so much that it contributes little or nothing to the final image, leaving the flash as the dominant or only meaningful light source. If you took the same shot with the flash off, it would be very dark or underexposed.

A common way to do it:

1. Choose the aperture you want for depth of field.
2. Set ISO as low as practical.
3. Raise shutter speed up to your camera’s flash sync speed to reduce ambient light.
4. If ambient is still too bright, use a smaller aperture and/or more flash power.
5. Then adjust flash power until your subject is correctly exposed.

Why do this? It gives you more control over the look of the light and can avoid color-balance problems from mixed lighting sources.

Important: shutter speed affects ambient exposure much more than flash exposure (within normal sync limits), because the flash burst is very brief. Indoors this is often easy; outdoors in bright daylight, fully overpowering ambient can be difficult with a small speedlight.