What the Accept Cookies popup is for and what data is being collected?

By clicking "Allow cookies" button a client confirms that he/she is acknowledged that this type of information is being recorded.

If we move beyond our extension scope we can say that cookies are collected by Magento itself.

Let's say you disabled cookies in your browser - you would not be allowed to make purchases at a particular store because Magento would always redirect you to the error page.

Therefore cookies are collected on all stores, not necessarily Magento ones and the bar that requests to accept cookies simply notifies that they are being collected.