When someone tells you that a mailing list is opt-in, they are telling you that the addresses on the list are there because they asked to be on the list.
There are varying levels of opt-in:
Simple opt-in is when a customer ticks a checkbox (or, more frequently, leaves a checkbox ticked) that indicates their willingness to receive messages from you.
Confirmed opt-in is when a subscriber requests to be on your list, you send them a confirming email message, and they respond to that message indicating that the original request was from them and they really want to be on your list.
Why do you care?
Addresses on confirmed opt-in lists will have a much higher delivery rate than simple opt-in lists, which in turn will have higher delivery rates than non-opt-in lists. With higher delivery rates, your messages are in front of more potential customers.