Enlist lets you tap an untapped creature you control when a creature with enlist attacks. That tapped creature doesn't attack itself, but it adds its power to the attacking enlisting creature, effectively lending muscle to one big swing.
The most common mistake: the enlisted creature doesn't need haste, since it's tapping but not attacking—so you can enlist a creature you played this turn. However, it must be untapped, and tapping it for enlist means it can't also attack or be used to crew/tap for other effects. Also, you only add the enlisted creature's power; its abilities (like deathtouch or trample) do not transfer to the attacker.
In Commander, enlist turns spare board presence into focused commander damage, helping push a single threat through for lethal or to pressure a key opponent.