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The side that asks and the side that answers
You type an address into your browser and a page comes back. In that instant, two players are each doing a set job.
The one that asks is the client; the one that answers is the server. Building something by splitting the roles this way is called a client-server system. The browser is the client, and the machine holding the page is the web server.
What matters is that the roles never swap. It is always the client that starts the conversation, and a server will never take it upon itself to push a page at you.
One more thing: server is the name of a role, not of a machine. One box can hold a web server and a database server together, and equally one role can be spread over many boxes.