I've seen some sites where the URL is like form.html?name=Bob&lastname=Parsons

How can you submit values only through HTML? Or if it uses another scripting language in association with HTML, how does it do this/how does this work?

Or maybe this could be some URL rewriting (mod_rewrite for Apache) at work?

they are appending extra information onto the URL to be used by the next page or script. if the info was done on a form, they used the GET method.

your example is probably going to a processing script done in PHP or ASP.

I don't think it can be done via PHP though? How would the logic work, could you explain?

form information gets submitted using the GET method.
info gets appended to the URL and directed to PHP processing page.
PHP script gathers the info via the URL and does whatever.