Well, I would still like to understand it. Given that the expression originates from the Old Testament, it exists in most (if not all) European languages. Both in English & Russian, the languages I know well, the preposition used in this expression is the same one that you would use describing a trade of something for something else. Is "um" the preposition Germans would use while negotiating a trade of A for B?
Is "um" the preposition Germans would use trading A for B?
Some (still?) do -- I think buying something um fünf Euro (= for the price of €5) is used in Austria. Duden ( https://www.duden.de/rechtschreibung/um_herum_vorbei_fuer#Bedeutung5 ) marks this use as "landschaftlich" (regional) without specifying where.
I grew up with für in that use, though, and I think that's the most common preposition among German speakers today.
I think Luther's Bible translation used um, so perhaps that use was more common several centuries ago. Also, the wording of most Bible-related sayings in German is based on Luther's translation.
If you're asking for the english meaning then in short it means "If someone rips my eye out I'll rip his eye out" and it's a fancy way to talk about revenge .
If you want the full story then this is a (translated) quote from Chamurappi's law - the oldest set of laws we know of and can still read today. It's characterized by it's strong emphasis on class hierarchy (for hitting a citizen you would get your arm cut off, for hitting a second class citizen you would have to pay a lot of money and for hitting a slave you would have to pay just a little bit of money) and it's leaning towards revenge based justice (if you kill a baby of someone from the same class he would have the right to have your baby killed).
Um means around
Prepositions are notoriously variable between languages and any attempt to map them one-to-one with an "X means Y" scheme is bound to fail.
Consider "for" in English -- does it mean "for the benefit of"? "I bought this book for my brother = I bought this book for the benefit of my brother". Okay. "I am waiting for you = I am waiting for your benefit" ?? Er, no.
So, what does "for" mean? Answer: more than one thing.
It means is some one with the same ranks hurt some ones eye or broke some ones tooth they will have the same treatment. Babylon has some impresive rules like if you attacked a free pregnant woman and caused her to lose her child you payed in gold (forgot the amount). Also if your crops went bad for a year your debts for that year were washed. And if you were a thief your punishment was death. There are like 200 rules left from the Babylon times. The first rules were found writen on a tall piller.