What is this copper ring insert in my sharkbite supply valve?
Here is the correct answer to the question as it is written. 

The copper ring is a ferrule, which is part of a compression fitting.

You absolutely need the copper Ferrule for a watertight connection, and plumbers tape is not necessary when this type of connection is installed properly.

If you do not know what a copper Farrule is and what a compression fitting is than you need to learn before you try to install this valve.

I have no way of knowing if you have the correct part for the plumbing task that you are trying to accomplish. If you edit your question with more details and photos then I may be able to help.