What is the function of this part/wire?

It seems as though the keyboard backlighting is in working order! Thank you for your help!

P.S. Is this cable removable from the keyboard?

Not unless you remove the whole backlight sheet from underneath the keyboard. Why?

And if your question is answered, kindly mark the answer as accepted to "close the case."

That was the second question that I had initially posted, and because it has now been answered, I will accept the answer to "close the case."

Thanks for your help! :)

Also to answer your question of why: I wanted to make sure that, if in the case that only the cable is replaceable, and if my keyboard backlighting does in fact act up in the future, I can replace it without much hassle. But because it seems like its not, I've concluded that this is not an option for me. Reassurance, if you will ^^

You can replace the backlight following this guide. It's a PIA specially because of the glued batteries, but feasible if need be. Once you reach the last step, you need to peel off the backlight sheet and install a new one. Of course, every time you gut a MacBook Pro like this, you risk damaging components and parts, specially if you like to dismantle it using a Dremel tool instead of good'ol screwdrivers. So don't start on any expensive machine like that unless you're going to be gentle and very patient. And never force it. If it needs force, then something is wrong: stop and re-evaluate.