A font server ideally stores the organization's entire font collection. The way that fonts are deployed from the server to the client varies by how each server is configured.
All of the servers will have a client application that connects to the server and includes auto-activation plug-ins for professional design applications. This client also allows the ability to preview, browse and search the font collection (whether the fonts are installed or not).
For example, with Universal Type Server, fonts can be replicated from the server to the client in three ways:
1. ALL - all fonts that the end user has access to (permissions controlled by the admin) are delivered to the end user when she connects
2. On-Demand - fonts are deployed to the end user only when activated, or previewed, and are cleared off of the end user's machine when not in use.
3. On-Demand local cache - fonts are deployed to the end user when required, and are cached for future use.
With many agencies having font collections that run into the tens of thousands, you can see how choosing the right setup can be critical.
Hopefull this helps clarify how font servers work.