At the bottom of the character map are codes for each symbol as selected. At the right is an Alt code, if there is one - this I understand. At the left is a code, and character description - e.g. U+005E: circumflex accent; and this I don't understand. Well, I know what a circumflex accent is of course, but it's the rest of it that puzzles me. The figures are obviously hexadecimal, but what does the whole thing indicate, and how is it used?
It's a system called 'Unicode'. You are right, they're hexadecimal. It was developed as universal character sets to let computers know just what it is you want to print.
Tells you about it (in more detail than you'll ever want to know!) here.