Servers deliver Web content to us clients. These clients might be you, other readers, even other computers. Different Internet services have different sorts of clients and servers, and different sorts of relations between the client and server. For example in FTP a connection is opened between the client and the server and that connection is maintained - kept open, a bit like when you ring someone up and they answer, the phone line between the two of you is kept open. The Web is quite different to this model.
Web servers are http servers.
That stands for HyperText Transfer Protocol. They are computers with software that allows them to receive requests from clients to serve web pages. What is different with http servers is that they are 'stateless' servers. A client requests a page, the page is sent, the server and the client then stop talking to each other. This makes http servers very efficient, and pretty dumb.