Speed is a stat in all three titles of the Mother series. It determines how fast a character or enemy is. 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, either of them could move first.
If, when a character succesfully evades an attack, it says "X dodged swiftly" or uses a similiar variant, this means that it was not through the 1/16 chance of Shoot attacks missing, rather because of their Speed.