Might is an effect that adds +5 to Strength and +1d10 to melee damage for its duration. There are a couple sources of Might:
Note that extending Might through any means will cause you to glow.
This effect is usually far stronger for monsters: it multiplies their damage output by 1.5, instead of simply adding 1d10. For this reason, one should exercise extreme caution around monsters such as moths of wrath, Rupert, or Wiglaf.
Tips and tricks
Might is useful for dealing with monsters that are troublesome, but for which Berserk or Haste would be overkill and/or unsafe - compared to those, Might has no drawbacks unless you extend it, so it's safe to use. It can be used when you need to kill an enemy quickly to prevent an emergency.