If a plant has fibrous roots it does not have just one root - it has lots of them. They grow out through the soil, hold the plant in place and take in water. There is no room in a fibrous root to store food.

You can see dried-up fibrous roots on the bottom of an onion. Each root grows out separately from the stem at the onion's base. Grass plants grow close together and their fibrous roots intertwine. This makes the layer of grass form a strong trample-proof surface. As the fibrous roots also hold soil in place the grass and soil can be dug up in sheets called turfs. Turfs are used for making new lawns and surfacing sports pitches.

The video shows you how a plant with fibrous roots can become potbound.