Why You Should Quarantine a Virus/Trojan
Quarantine does what it says. It will wall off the infected program and make sure that it can't affect the rest of your system. Most antivirus software will do this through a special virus chest that you can access through the program.
You're basically safe once the virus or Trojan has been quarantined. If your program is any good, then that infected file is as good as if it had been deleted. It is still on the system though and you will probably want to wipe it out at some point in the future.
Why should you quarantine a virus/Trojan? Well, there are some benefits to a temporary quarantine. The big benefit is that you still have a copy to play around with, but it's in a safe format. You can check the name and analyze it a little more.
Once a Trojan or virus is quarantined, you should do some quick Googling for the name. There are a few good databases of viruses out there. What you really want to get is confirmation that it's infected. A lot of antivirus programs will have occasional false positives. I had one a few months ago, where the DRM on a steam copy of X-COM was enough to trigger an alert. Until you can confirm that the file is really infected, you should just quarantine it. If it's a false alarm, then you can restore it to it's rightful place.
Of course, there isn't much of a reason to just leave a virus in the virus chest either. Once it's confirmed as infected, you should really delete it.