I bought a refurbished iPhone that has the Cydia icon on it. Does that mean it is already jailbroken? If so, can I just go ahead and use the apps? Do I have to jailbreak to use it? Also the iPhone is used on my Tmobile provider and I was told not to update the iOS on iTunes or it will get locked to ATT and I will not be able to use it.
It certainly sounds like it's been jailbroken, and unlocked with one of the tools rather than by authorised means.
If Cydia works, then it's been jailbroken and there's nothing you need to do.
The downside is that if you're not aware of the unlocking tools, or how to jailbreak in the first place, you either need to start researching these, or avoid doing any official software updates.
There are a great many sites which have guides, some good some bad, and some downright dangerous. I'd recommend http://osxdaily.com and http://blog.iphone-dev.org as the most reliable of sources. The former being a site which reports on developments, and the latter being the people who release most of the tools.