A lighting modifier is designed to change the character of the light from a flashgun, or some other source of artificial lighting. Mostly they soften or diffuse the light, or change its direction.
The most common type of lighting modifiers are the softboxes, brollies, honeycomb grids and other accessories attached to studio lighting systems. However, it’s also possible to get lighting modifiers that attach to regular camera-mounted flashguns, providing a reflective surface for bounced flash or a mini-softbox for smoother and more even lighting.