A server is a computer (or software on a computer) that is listening for Internet requests so that it can "serve" back responses. Some of those responses might be static assets or the server can execute a programming language to respond with a dynamic response.
Unless your company is similar to Google.com where you can afford your own server data-centers, you're probably going to lease servers from a third party company which will be your website host.
The main server (or cluster of servers) where the programming languages execute or the static assets are uploaded to is called the "origin server". Sometimes origin servers distribute their contents all over the Internet to "edge servers" to create faster download experiences for users. These are also called CDNs.