What does Umbrella insurance really buy for me?

Already have pretty good coverage on auto (multiple cars), and home (one). Do not own commercial property/business, etc.
Under what scenario does umbrella coverage really kick in, and in the relatively straightforward case such as mine, it is worth it?

Thanks for your advice.

Consider this scenario. You cause an accident which puts someone out of work for the rest of their life and causes very high medical bills. The courts can take everything except one car, basic household furnishings, the value of your house over $150,000 (which means if your house is valued higher you might have to sell), and up to 30% of your wages for the rest of your life.

Do the math. Figure the amount of your assets and estimate 30% of your future earnings. That is what is at risk. Now figure if the premium for an unbrella is worth it.