Bite Omen Card (and other similar cards)
It means that you get attacked following all the normal rules of an  attack from a person or monster with a might of 4. The person to your right is simply taking the role of rolling the dice.

So he will roll 4 dice, and you will then roll dice equal to your might. If his total is greater than yours, you will take physical damage equal to the difference of the rolls. If you tie or win, nothing happens.