In principle, any computerized process that can be used or called by another process (particularly remotely, particularly to share a resource) is a server, and the calling process or processes is a client. Thus any general-purpose computer connected to a network can host servers.
Your computer and the related server software must always be running to be accessible. When your computer is used as a server, its resources (e.g., processing and bandwidth) is taken away from what you have available to do other things.