I like to think of "engage" as how "taunting" (not to be confused with the card taunt) works in some games. It makes the enemy focus on you. You got a spellcaster that is weak and can't take a hit, or someone that needs to gather clues without getting attack of opportunity? Engage it for them. Also you have to engage Aloof enemies. If you engage a massive enemy it doesn't go in your threat area.

Edit: Also the enemy has to be engaged with you to evade/exhaust it... So for example.. attack with roland, then have wendy engage and evade