An eyeball mirror is something that refracts and focuses light into your eyeball in a different way so you can see better. Really, these things are glasses, not eye mirrors, but same sort of things when you get down to it. Just imagine someone wearing mirrors on their eyes, and when you ask them what those are for, they just say they're glasses.
The reading for 眼 is the same as the vocab 眼. The reading for 鏡 is an exception, totally different. It shares a reading with 金 (gold), though, so think of the mirrors on the person's eyes being made of gold. What nice glasses!
This word can also be read as がんきょう, but usually only on official/written documents. If you're speaking and not reading a government document, you should say めがね!
You should wipe your glasses.