Q: What is supervised and un supervised?

I'm not sure what you mean by supervised and unsupervised, however you cannot upgrade to iOS7. That OS is not currently signed by apple.

Supervised is something you'll probably never have to worry about. See article below.

http://www.classthink.com/2013/10/15/supervised-ipads/

You should be able to update to ios 7 if you wish.  ios 7 is the highest version of iOS that runs on the iPhone 4.  I have ios 7.1.2 on my iPhone 4 and have not experienced any problems.

Supervised is used in schools and businesses to place global restrictions on the device.  For personal use, don't worry about it.

R

I'd like to gather bits and pieces of the above responses and try to present a single source of information.

Assuming you are inquiring about an iPhone 4, then you should be able to update to iOS 7.1.2, which is the latest version of iOS the device can run.

But if the device was supervised (i.e., owned by something like an educational institution), you may not have the freedom to change much without the consent of the IT Department.  Read more about supervised devices here:

How to tell if an iPhone, iPad, or iPod touch is supervised - Apple Support