Speed is a stat in all three titles of the Mother series. This stat determines who moves first during a battle. In most cases, the character with the highest speed will move first, but if two characters have equal or near-equal speed, the character to move first is chosen randomly.
Speed also affects a character's ability to dodge in battle. If, when a character succesfully evades an attack, it says "X dodged swiftly" or uses a similiar variant, this means that it was because of their Speed, rather than through the 1/16 chance of Shoot attacks missing.