In Bonfire, a character's Speed attribute determines not only the turn order, but also how frequently a character can act. A faster hero like Nadia can move several times for every action taken by a slower character, for instance.
Each unit has a hidden Turn Progress stat that starts at 0. Action is taken when this stat reaches 100. Every time the game has to find the next actor, it goes through all units and adds points to their Turn Progress according to this formula:
Turn Progress += 20 + 0.24 * [Character's Speed]
If 100 hasn't been reached on any of the characters, the game repeats the process until someone does. If multiple units reach the threshold, then the one with the most points acts. Upon completion of an action, 100 points are deducted. Excess points are not wasted and contribute towards future turns.
Some abilities can affect turn order directly by quickening or delaying some characters. See the Ability Power page for more details.