When you create a computer network you must decide if you are going to adopt a peer to peer approach or a client server approach
Peer to Peer
Each computer administrator has control over the resources of that computer.
Advantages
Cheap
Lower barrier to entry (no additional administration skills required)
Easy to setup
Disadvantages
no control over security (administrative nightmare if the network grows)
no centralized control over file access
Client server
The server is in control of all the resources of the network, changes made once on the server affect all the clients immediately
Advantages
centralized control over security
centralized backup
easier to manage the resources on the network
easier to control access
supports growth into a larger LAN without having to change the core
Disadvantages
More complex, requires some skills to set up and maintain
authentication traffic can slow the network down to come extent
Services
Any node on a network that provides a service to the other nodes on that network is a server. If you have shared your printer on you home computer network so that your parent can print to it from the computer in the next room then you have made your computer into a print server.
Many different services can be offered by nodes on the network. Some of these services will be provided by dedicated computers with massive processing power and huge disk arrays, but some services can be provided on low powered devices that have very little in the way or resources.
Here is list of some of the services that are probably offered by your school servers:
file storage (you probably have a home directory where your personal data is stored on the server)
print (you can print to many different printers that change according to where you are)
authentication (you must provide a username and password in order to gain access tot he network)
proxy service (all your requests fro web pages are routed through this server that handles all interactions with the outside world)
database server (MYSQL and SQL are database servers, one of which probably provides the data for your school administration system)
Application server (in cloud computing the application that you are using to interact with your data is run on the server, SAAS(software as a service) is commonly associated with cloud computing)
name server (DNS - this will be able to take the url that you typed in and convert it into an IP address so that the packets can be correctly addressed)
Web server(every time you load a web page into your browser you are calling on the services of a web server)
email server- if your school uses Microsoft exchange server then you are using an email server
On line gaming - this service is unlikely to run on your school LAN but you will probably have connected your multi-player game to it's on line server in order to play against other gamers over the internet.
Chat and Instant messaging servers - apps like BBM, whatsApp and Kik messenger all rely on a server to rout the messages from your device to the intended recipient.
Media server - a device that serves up video streams to requesting clients
These are just a few, many more are possible and more new server types will be invented as new programs are written that require them