For example, you walk into your kitchen, flip a switch, the ceiling light goes on and the room is lighted. Task lighting is, as the name implies, lighting for a particular task. In the kitchen, it would be the under-cabinet lighting that illuminates the counter top. While the ceiling fixture provides general light to the room, the fixtures mounted beneath the upper cabinets light the countertop sufficiently for food preparation. Similarly, you might install a light above the sink so that when you are washing dishes during the evening, you will be able to see what you're doing.
Accent lighting is used for decorative purposes.
This might be a fixture that illuminates a painting hanging on the wall or, to go back to the kitchen, lighting placed on top of the upper cabinets to wash up the walls and onto the ceiling. While these fixtures will contribute to the overall level of light in the room, their main purpose is aesthetic. They either call attention to a decorative item or architectural detail or they create a decorative effect by themselves. A good design usually combines all three types of lighting, using a variety of fixtures. Indirect lighting uses a fixture that is hidden, often behind a valance or molding, so that only the light, but not the source of the light, is visible.