What does the term 'glycogen mobilisation' mean?
I think the key to understanding mobilization in this context is in the second sentence:

[Glycogen] can be broken down to yield glucose molecules when energy is needed.

The authors are using mobilize in a figurative sense to suggest that glycogen can be quickly and efficiently metabolized to suit the energy needs of the body, like an army may be mobilized to fight a war.  See definition #2 on Wiktionary:

mobilize (verb)
2. (transitive) To assemble troops and their equipment in a coordinated fashion so as to be ready for war.