So how it'll work is, you'll still gain levels as normal and higher levels = more HP/MP and more damage (level is used in damage formulas and more besides). Where Rank Up comes in is with the character's actual stats like Strength, Magic, etc. These now stay static and won't increase when leveling up, instead players boost these stats through Rank-Up.
Whenever a boss is defeated, or certain story events are completed, each character gains SP. When SP passes certain thresholds, the character gains a Rank and when you next visit the Emporium you choose which stats to improve for the character.
There are 8 ranks per character and they each give the same three options to boost that character's stats. So for instance the options could be:
1) Strength/Magic/Vitality +10
2) Strength +20, Dexterity +10
3) Magic/Spirit +15
You can take any option at each Rank, so you could pick Option #1 three times and then Option #2 five times, or you could just pick Option #3 eight times, etc. The idea is that you can build a character in different ways, either pushing certain stats all the way or rounding out weaknesses, etc.
