The primary way that animals, or more specifically, animal cells store glucose is in a compound known as glycogen. Glycogen is primarily stored by liver cells, but some is also stored in muscle cells for immediate use if needed. Glycogen molecules consist of many thousands of glucose molecules linked together by alpha acetal groups in a highly branched, very compact form.
Glucose is the primary fuel the body uses to create adenosine triphosphate, or ATP, the energy currency used by every cell on the planet. The brain, in particular, is almost totally reliant on a steady stream of glucose for operation. The muscles must also be ready to use energy at a much higher rate than digestion and circulation can provide. Glycogen is the body's way of keeping a quickly accessible form of energy on hand for these vital systems.
The body's capacity to store glycogen is limited. The liver and muscle cells can only store so much. When there is excess, glucose is not stored in glycogen, but is instead converted into fat, another form of compact energy storage, but one that takes longer to utilize than glycogen. Muscle cells use calories from digesting food or fats when energy demand is low, using their glycogen for more intense efforts.