A server computer or server software? (There is a product named FileMaker Server which is one, not the only option for hosting a FileMaker database over a network.)
Whether you need a server or not depends on one you plan to do with FileMaker.
I am to perform Filemaker across the network. do I need a server for it? thanks
Maybe. Maybe not.
FileMaker Pro can host up to 9 simultaneous FileMaker Pro clients and up to 5 simultaneous Web browser clients if you set up your database to publish to the web with Instant web publishing.
FileMaker Server and FileMaker Server Advanced support many more clients at one time and also offer additional features to better support managing a hosted database. The Features and hardware requirements are available from FileMaker's Product Information web pages.