I don't think she'll be able to use the days on that ticket for the Animal Kingdom - there's some weird rule about that.
As for the rest of the parks, it should be fine. She might want to take it to Guest Services and see exactly how many days are left. (Unless she's like my dad, who attaches a post-it note with the info on every ticket.)
The paying is if you want to upgrade/add those days onto another ticket. Like, say you have two old hoppers with 4 days total left. You want to combine those two and get a 5-day hopper. Guest Services would credit you for the four days (at the price you paid for the original tickets, I believe) and you would pay the difference for the fifth day. That way you wouldn't be carrying around two old tickets and one new one. Convinent for some people, especially if you have several old tickets.