If something is called grievous, you better take it seriously. Grievous is used to describe horrible things like tragedies or crimes. If you have a grievous wound, a band aid simply won't do.
Grievous is derived from the noun grief, which means "sadness." When something is grievous, therefore, it's not just bad, but so bad that it causes unusually intense shock or sadness. It's often used to describe crimes and other bad deeds that go beyond mere criminality and into the world of cruelty. For example, it's harmful to steal from someone; it's grievous to steal from them and then, having stolen their stuff, beat them up or kill them.