What are the differences between glycogen, starch and cellulose?

All three of these are carbohydrate polymers, formed from glucose monomers.

Glycogen and starch are both polymers of alpha glucose. These long chains of alpha glucose molecules, joined end-to-end, form a spiral, or helix structure. In addition, the chains in starch and glycogen have a branched structure, i.e. each chain can fork into two.

Cellulose on the other hand, is a polymer of beta glucose, and so the polymer forms straight/linear, unbranched chains.

These differences in structure underly the different functions of these molecules. Starch and glycogen are used as energy storage molecules - starch in plants, glycogen in animals (and fungi and bacteria). The helical chains and branching give these molecules an open structure, which means they are easily accesible by enzymes, and so can be broken down (or assembled) quickly.

The straight, unbranched chains of cellulose (made by plants) can pack close together to form long fibres, which are not easily broken down. Cellulose has a structural role in plant cell walls - it is an important component of wood, for example. Cotton is almost entirely cellulose.