With Node.js you have Javascript as a serverside language (like PHP, Python, etc). But included with it you have a library that allows you to create a webserver.
Instead of having a webserver and couple a serverside language to it, you have a serverside language that is able to spawn its own webserver (although you can choose to use Apache or others).
The biggest advantage though, comes from the fact that JS is a functional language with a focus on event based programming. And so Node.js follows that paradigm: you use JS functions that are binded to certain events and run when one event happens, instead of running continously and doing some kind of loop waiting on I/O,CPU, database, etc. This allows for better performance.
Plus there's the advantage of being able to program websites using the same language both client-side and serverside. But thats another matter.
-- MV