This is just a way of saying how much light a lens can capture when the aperture is fully open. Zoom lenses often have a range of values, such as you've quoted, because the amount of light they can capture changes slightly depending on the zoom setting. You don't need to pay any attention to this when you use the lens - certainly it isn't telling you to only use the lens over that aperture range.

The reason it's important is:
1. Lenses that can capture more light are better at shooting in low light conditions (there are other differences too, but that's the main one).
2. Lenses that can capture more light cost loads more! For example, look at the cost of a 200mm F2.8 lens compared to a 200mm F4 lens - the former lets in twice as much light but will cost you a lot more, and be bigger and heavier because the glass elements need to be so much larger.