The server computer can be anything that is capable of storing and 'serving' files. It does not have to run Windows, but there are benefits if it is Windows based.
In small networks of up to 10 users, it does not need to run a 'server' operating system, any modern Windows PC will do, e.g. one running Windows XP Pro or above.
Match-IT needs nothing on the server beyond a network aware operating system. Any PC you bought recently would be more than adequate.
The server stores the program and the databases. If it's a Windows based server, it's also used to run the 'Agent'. This is a housekeeping service that normally runs during the night, so the server PC needs to be left switched on all the time.