Fire Emblem Heroes has 4 distinct move types:
Infantry - Units who can move up to 2 spaces at a time, but are slowed by forests.
Armored or armor(s) - Units who can move only 1 space at a time.
Cavalry or cavalier(s) - Units who can move up to 3 spaces at a time, but cannot enter forests. They are also slowed by trenches.
Flying or flier(s) - Units who can move up to 2 spaces at a time, are unaffected by forests and can fly over mountains, pits, and water. However they are weak to bows.
Movement types also affect which skills can be inherited, and the unit's Stat Growth.