The word "first" (in many cases) means the badge will only be awarded the first time the criteria are met. This is contrary to the Nice Answer series, for example, which will be awarded for each time the criteria are met.
I was also confused as a new user and apparently still am. I think it could be cleared up by appending "(Awarded once)" to the confusing descriptions instead of using "first". The enlightened badge, however, should still say first because it indeed means "first answer" (thanks TheTXI).
For example:
Enlightened - First answer and was accepted with at least 10 upvotes
Scholar - Accepted an answer on your own question (awarded once)
Student - Asked a question with at least one up vote (awarded once)
