Servers fulfill one main purpose. They serve as a focal point for data that is manipulated or accessed by multiple computers/users. As well, they often support certain shared network peripherals. In a multi-user system they are indispensable at making data available simultaneously to users that don't want to be dependent on other users having the same data available, or not available when their workstation is shutdown.
If you have been getting by without having a server, you may not "need" one, but it does have advantages, especially in networks where you don't want to have so many workstations running, because your data is spread out.
Servers also permit a much less expensive data backup strategy.