I was wondering if someone could help to understand what this sentence means so I can explain it better. This is the sentence on a coupon.

"Redeemable by addressee only, or with corrected address information and a Valid ID"

The sentence is supposed to mean that the coupon is redeemable by one or the other...either way you must have a valid ID.

Can someone help explain why it means this (above) or why it does not?

I can't get there. It's because addressee has the idea of a person and the right address woven into one word. To divide these into separate ideas you need a longer construction. The version below isn't that clumsy, and it's pretty clear:

Redeemable only by the addressee. (If there has been a change of address, a valid ID is required.)