Declining a penalty is when the team not receiving the penalty turns down the penalty on the other team. Penalties usually result in a loss or gain of yards and a replay of the down.
Example
If the offense runs a play on third down and ends up four yards short of a first down but commits an offensive penalty the defense would most likely want to decline that penalty so that the third down play stands. If they were to accept the penalty the offense would get another shot and making the third down yardage even though it would be 9 yards to go (5 yard penalty) or 14 yards to go (10 yard penalty). Even though the penalty would back up the offense why give them another shot at completing third down yardage. Declining the penalty makes it fourth down with four yards to go and they most likely punt.
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it means that the penalty the other team had, you don't want the yardage to be added on. Say if it were third down and ten, and the offense didn't get the first down. I would decline the penalty so it would be fourth down. the team would most likely punt the ball to you
that you don't enfore what the penalty is such as if there is offsides on defense but i score i would decline and go on as if it never happened.