The client/server model is a way to describe an architecture, a relationship between machines and services. The client is the machine which asks for something (a request) and the server can send the results of the request back. The server is passive, until it receives a request.
For instance a user wants to browse a website, e.g. Youtube.com. S/he types in the url and the machine becomes the client. The request turns in to a quite complicated chain of IP-adresses and more, but is finally received by a server, which sends back the answer to the request. Sometimes the role changes and the server turns into a client and ask for information from other servers.
Today in the world of the Internet, it can be difficult to imagine something which is not client/server (see the link to the film "Warriors of the net" ). Example of non client/server-system are local PCs or mainframes.
So, the client is a machine, which can ask for something, the server is a machine or service, which can return something, e.g. a website, database request or the like.
A user accesses a social media service like Google+ or Facebook. On this service, a Youtube-clib is embedded. Try to describe this scenario as a client/server-architecture.