Gizmodo has a video showing it in action. It allows you to to select text from a webpage (including hyperlinks on the web page) and paste it either into mobile Safari or into an email in the iPhone's Mail application. I didn't see in the video if this service allowed you to copy the URL you are currently on. I don't think it does allow that, in which case it's a little bit limiting
There have been some third party applications that offered some sort of copy and paste for the iPhone, Pastebud will be the first to provide the functionality without having to install any software on the iPhone.
Don't expect something for nothing though. With copy/paste in such high demand on the iPhone, it appears Pastbud will display popup ads. In the Gizmodo video a popup says, "Thank you for trying pastebud! Upgrade now to make it even more convenient, for just $5."
I should also add that security / privacy is a concern. You're sending what you copy/paste to Pastebud's servers. I guess you best not be copy/pasting any confidential info.