Offensive Interference is when the batter or a runner interfere with the defense's ability to make a play.
Interference on a Batted ball.
Batter is out for interfering with the catcher on a pop-up in foul territory. The fielder always has the right of way over a runner when attempting to field a batted ball. The only exception is a popup over a base occupied by a runner with less than 2 out. The runner in that situation is allowed to stay on his base even if it causes difficulty for the fielder. Ignore the announcer's comments about the batter's box; in this situation, the batter must vacate and allow the fielder to make the play.
Runner at first base collides with 2B and is called out for interference. Ball is immediately dead. Batter placed at 1B and the other runners are returned to their bases.
Here the fielder makes the play on a popup in spite of interference by the runner at first. This is not a double play. The ball is dead as soon as the interference is called, so the runner is out and the batter is placed at first base.
Runner hit by batted ball and is called out for interference. Ball is dead, batter placed at first and runner at third stays at third.
The ball does not have to hit the runner in order for there to be interference, nor is a collision required. Running in front of the fielder is sufficient.
Again, immediate dead ball, interfering runner is out, the runner at third has to go back to his base, and the batter is placed at first.
Batter out for interference when ball hits him after a bunt. BOTH feet have to be out of the batter's box when the ball hits the batter for this to be an out. If either foot is still in the box, it is a foul ball.
The batter is not entitled to a direct path to 1st base if that is where the ball is hit (same goes for runners between bases). Whether or not this batter-runner is touched by the ball, he interfered with the catcher fielding the ball and is out for interference.
Batter's Interference is when the batter interferes with the defense's ability to make a throw or play (generally we are talking about the catcher as the player being interfered with).
Batter interferes with catcher's throw. If the batter keeps both feet in the batter's box, they generally cannot be called for interference. Since this is strike 3 the batter is already out and so the runner is called out as punishment for the interference.
A more typical example of batter interference. The batter is called out for interfering with the catcher's throw. Dead ball, runner sent back.
Runners interfering with throws
A runner is generally not guilty of interference if they are hit by or otherwise impede a fielder's throw, but there are special cases where they can be called for interference.
Running Lane Violation
On a ball hit in front of home plate, the batter is required to run in the lane. If the batter-runner is outside the lane and is hit by the throw or otherwise interferes with a quality throw, they are out for Interference. Again, interference is a dead ball and the runners go back to their bases.
Team member not participating in the play
An offensive player that is already out (or a coach) can be held liable for interfereing with a throw. Here the batter is already out after the popup is caught and when the throw hits him, the runner is called out for the retired batter's interference.
If an offensive player does something intentional to interfere with a throw, that is also interference. Here the runner puts his hand up to block the throw and the defense is given the out at first for this interference.
Another type of intentional act by a runner that is interference. Batter-runner is out and runner has to go back to first on dead ball.
Another jerky play that is interference. The umpires didn't call it here, but yelling at the fielders to distract them is interference