The existance of a wizarding school alone tells you certain things about the setting - that magic is common enough for a school to be viable, that it is well enough understood to be taught, that it is tolerated sufficiently for a school to be practicable and that there is a means of identifying those who can be taught (or that anyone can be taught magic).
The profile of the class and faculty will have a big impact on the nature of the place - if a student wizard is expected to take to magic only after a full basic education, it is likely to be a smaller and more earnest place, probably attached to a mundane university; if magic can be learned in childhood then it is more likely to resemble a (very dangerous) school. A common alternative is to add a 'School of Magic' to the other schools at a university, making it an undergraduate subject (BSoc anyone?). It will be a very wierd world indeed if magic is 'just another subject' in the education system.
Staff and pupils have the potential to be very wierd indeed, given the typical nature of magic the school could well be one place where non-humans barely raise an eyebrow - expect also a variety of magical servants such as golems, animated objects and homunculi wandering about.
The curriculum also bears examination - expect a school to teach only "white magic" (whether the disitinction actually exists in your setting or not) "grey magic" and "black magic" may be studied rather than taught, reserved for advanced programmes or completely taboo. Frequently contentious areas of mainstream magic will also not be taught for various reasons. A school which disregards these conventions is better suited for less traditional grey and grey morality settings.
The school may - or may not - also teach potion making and the like.
No-one should be at all surprised if a wizarding school turns out to be an Academy of Adventure - in fact it's probably the default source of such places. Whether the wizard training is cause or effect of the school being less than sedate will depend on your setting.
You may also expect the architecture of the campus to be … unconventional. It doesn't have to be, but if anywhere is going to have alien geometry, lakes of magma and literal ivory towers, this is the place. A great deal of effort may be necessary to keep the HSE from finding their way onto site.
The normal alternative to a "wizarding school" is the apprenticeship system, whereby individual wizards take on and train pupils by themselves - in some settings this runs alongside formal schooling in a more or less feasible manner, in others this is how renegades learn their magic and/or part of the history of the system. In the "historical" case, a trainee wizard might still be termed an apprentice.
Expect a magic school to be fairly elitist in most settings, to have a strong espirit de corps and - usually - to have a rivalrly with at least some rival schools. Graduate wizards may wear a specific set of robes to identify themselves. Different schools may teach completely different curriculae and even philosophies of magic, which can lead to "battling kung-fu syndrome" when their allumini meet each other.
Game and Story Use
- A great venue (for an all wizard student campaign), patron or source of work for any suitable campaign.
- Also, potentially a rival or villain.
- Possibly all of the above.
- An unstable enough school might well have a full time team of troubleshooters on hand to deal with the consequences of student errors.
- A magic-using character might be a graduate of such a school