Have read a lot of references to graph databases, but don't really understand how to implement it in real life. Is graph database a concept or an actual database?

Any good resources to how to setup a basic graph database and its practical use, like a hello world example?

I'm also thinking whilst facebook has a lot of data, it doesn't retrieve all of them but only the minimal. So it's still possible to use traditional MYSQL database as long as they're sharded extensively?