Defensive Interference is when a defensive player interferes with the batter's attempt to hit the ball, commonly known as Catcher's Interference. Depending on what happens, it can result in an immediate dead ball or a delayed dead ball.
Immediate Dead ball
In this example, the ball is fouled off as the bat hits the catcher's glove. Ball dead, batter awarded 1st. You can clearly hear the umpire say "Time out. Time out. Catcher's interference"
The ball does not have to be hit by the bat for there to be defensive interference. This should have resulted in the batter being given first base.
Delayed Dead ball
Catcher's interference on ball put in play, delayed dead ball. Umpires let the play go to conclusion and then award the batter first base. Runners go back to their bases. Since there are two outs, there is no option to decline the catcher's interference (next video).
Catcher's interference on ball put in play, delayed dead ball. Umpires let the play go to conclusion and then award the batter first base. Runners go back to their bases. BUT the offense has the option of declining catcher's interference and taking the result of the play. This video shows two plays where the manager declined the penalty because the play scored a run.