Mila's Turnwheel is a brand new mechanic to the Fire Emblem Series, and what a useful one it has become. It allows a player to, at any point during a player phase, turn back time to anywhere in the battle. This is key if you make a mistake, but it can also be used to re-roll the random number generator. If your attack that you needed to hit misses, you can use Mila's Turnwheel to do it over again, increasing the chance of landing it.
Mila's Turnwheel can also be used to evade enemy attacks, but be careful not to waste all of the Turnwheel's limited amount of uses on trying to get an unlikely crucial or survive a foe's lethal attack. It might be better to turn back farther and instead rethink all the moves you made leading up to the situation you are trying to avoid. Use the Turnwheel especially conservatively while in Dungeons, as its uses will not be restored between battles inside of such.
Finally, Mia's Turnwheel cannot save a player if Alm or Celica dies. If this happens, you will get a game over without getting the chance to use the Turnwheel. So don't put them in a potentially harmful situation, because you won't be able to undo the effects of it.