The intended function of a server in web hosting is to store, process, and deliver web content to users over the internet. Servers operate by responding to requests from client devices, which can include computers or smartphones, retrieving the appropriate data, and serving it in a format viewable by the user. This process involves various components, including databases, application logic, and network protocols. Effective servers ensure high availability, reliability, and speed, all crucial for a positive user experience in web applications.