Court Reporters?

I've only been to court once, when I was still a medical student and my professor in Legal Medicine wanted us to see a live court proceeding. We arrived early, so we were able to observe some other cases before our professor was called in as an expert witness to some medico-legal case. It's pretty interesting, actually. Some cases are even funny. I was (and is still curious) about the people in court. Of course, there's the judge, the plaintiff with his lawyer and the defendant and his lawyer. We don't have a jury system here so no jury. I wonder what the so-called court reporters actually do? Do they type up everything that's being said in court? Do they describe the appearance of the people involved?

Is it advantageous for somebody to actually hire somebody to record the proceedings? This last question is because I've come across a site that says that you can hire court reporters. If you're as curious as I am, or if you need one, check out the link.