To understand what mod_rewrite does you first need to understand how a web server works. A web server responds to HTTP requests. An HTTP request at its most basic level looks like this:
GET /foo/bar.html HTTP/1.1This is the simple request of a browser to a web server requesting the URL /foo/bar.html from it. It is important to stress that it does not request a file, it requests just some arbitrary URL. The request may also look like this:
GET /foo/bar?baz=42 HTTP/1.1This is just as valid a request for a URL, and it has more obviously nothing to do with files.
The web server is an application listening on a port, accepting HTTP requests coming in on that port and returning a response. A web server is entirely free to respond to any request in any way it sees fit/in any way you have configured it to respond. This response is not a file, it's an HTTP response which may or may not have anything to do with physical files on any disk. A web server doesn't have to be Apache, there are many other web servers which are all just programs which run persistently and are attached to a port which respond to HTTP requests. You can write one yourself. This paragraph was intended to divorce you from any notion that URLs directly equal files, which is really important to understand. :)
The default configuration of most web servers is to look for a file that matches the URL on the hard disk. If the document root of the server is set to, say, /var/www, it may look whether the file /var/www/foo/bar.html exists and serve it if so. If the file ends in ".php" it will invoke the PHP interpreter and then return the result. All this association is completely configurable; a file doesn't have to end in ".php" for the web server to run it through the PHP interpreter, and the URL doesn't have to match any particular file on disk for something to happen.