|This article is about the current version of DF.|
Military dwarves watching demonstrations will gain Student experience in addition to gaining experience in combat skills. Presumably, dwarves that are good students learn faster from these demonstrations.
The dwarf leading the demonstration gains teacher experience, which also probably affects learning rate.
Guildhall demonstrations similarly train Student skills slowly. Engineer Guildhall can also hold Studying Demonstrations, allowing a Proficient Teacher/Student to train unskilled dwarves to Proficient Student in six weeks.
The student skill can be raised slowly by reading certain books throughout the world. It seems books written by scholars (as opposed to necromancers) are the only ones that increase the student skill. It's currently unknown what effect (if any) a higher student skill has on gameplay in adventure mode.