What does reversed and rendered mean?

Reversed and rendered is a term a higher court, such as an appellate court uses. Basically it means that the judgment in the original court (trial court) is reversed or is now in favor of the party who won the appeal. This phrase also means that you can't pursue the case again. An exception to this would be another appeal.

Example.

Sally sues Bob for hitting a baseball in her house. Sally says he did and Bob says he didn't. No other witnesses. A judge decides Bob is at fault and orders Bob to fix the damages to the house. Bob appeals and an appeals court reverses and renders. This means, Bob is no longer at fault AND Sally can't sue him again for throwing the baseball, ie. there is no trial. However if the case was reversed and remanded or a mistrial declared that will usually result in another trial.