A server is nothing but a computer which is connected to network resources and managed heavy tasks such as running web applications etc. Technically all the computers are capable of becoming a server but you have to upgrade the hardware resources and you need to have a dedicated IP address for accessing your server.
There are many categories of server such as web-servers, database-servers, and network-server.
Nowadays Web Server comes with a large number of packages related to the Internet- and intranet-related programs for serving emails, downloading content from websites, managing server resources like how much resources will your websites need to perform at its best, security proof like preventing your websites from cyber attacks and backing-up your data also.
Database Servers are basically used to store the data and retrieve the data from the websites. Basically, the database server is connected to the web server for their I/O operations. Examples of database servers are MySql, MariaDB, PostgreSQL, MongoDB, etc. It basically depends upon the developer which database server will be beneficial for applications.
Network Servers are usually used to store your images, files, which is used as the central repository of data and various programs that are shared by users in a network. Suppose you have an old computer at home and wanted to use as a network server then you can use it, you will just need to connect the computer to your home internet and all the people who are accessing the network can access the data from the network.