What does it mean in football when a penalty is declined?
The opposing team (team receiving the benefit of the penalty) has the option of taking or declining the penalty. There are actually times when the completed play would actually be worth more than the penalty. Take for instance that the penalty gives you 5 yards 4th down but the completed play resulted in 20 yards 1st down. In this case, you would want to decline the penalty and take the completed play.
When a penalty is declined, the opponents of the team against whom the penalty is assessed choose _not_ to take the yardage they would have gained by accepting the penalty. This quite often occurs if the penalty yardage gained is less than the result of the play when that penalty was assessed (Jon Perryman provided an example), or if the play results in a touchdown despite a penalty by the team scored on.