This is a great question. The interrupter, along with the shell stop, are confusing parts. Old Mossys reply is great. We will explain these parts a little more with moving pitchers! Todays model is the handy-dandy 590 Mariner. We've swapped in matte parkerized parts for contrast.
The task of the cartridge interrupter is to keep shells in the tube when the shell stop is out of the way. Plain and simple. Without the interrupter the magazine tube will spit up all the shells at once as we'll see. The interrupter is blocked by the locking block and rotates on a pivot. This is why it cannot be staked in place like an 870.
Here's something I found looking around,,,,
Dealing with double feeds , late feeds, and no feeds of the shell/cartridge from the magazine of the Mossberg 500 and other shotguns is a matter of controling the shell/cartridge stop and the interruptor. (info below assumes a clean gun)
On the Mossberg 500 series guns the stop is on the inside left panel of the receiver and the interruptor is on the right side internal panel. They are held in place by the trigger housing and are easily removed (or fall out) when the housing is removed from the receiver .
The cartridge stop is actuated in and out by a small tab protruding upward near the front of the stop (just back from the front curve) as it interacts with the left slide action bar . (tappered ramps meet during the feed cycle and pull the stop to the left releasing the shell from the magazine. When the bolt is forward, the shell stop is allowed to be at rest and hold the shell head to prevent shells from coming out of the magazine tube.
The cartridge interruptor is actuated up and down on it's pivot with its interaction with the bolt slide. The front of this interruptor moves downward during the feed cycle to prevent the second shell in the magazine from coming out . (double feeding). When the bolt is forward the head of the interuptor is held out of the path of the shell head in the magazine allowing it to push up against the shell stop where it is held in place. (read above)
The most frequent adjustment needed in this sytem is with the cartridge stop. If not adjusted properly it will allow the shell head to pass out of the magazine at the incorrect time, or it will hold the shell into the magazine when it is suppose to release it into the action. Since there is some variation allowed in the diameter of the shell base in catridge manufacturing there are times that changing brands, or lots ,of shells can correct feed problems. A much better way however is to correctly adjust the stop so that it will reliably feed all brands having some tolerance built into the gun by adjustment.
To adjust the shell stop you should first observe its range of movement during operation. You can use dummy rounds, feeding them with the gun held upside down to observe how the end of the stop mates with the base of the shell. With the bolt forward there should be sufficeint engagement to hold the shells into the magazine.(even when wiggled slightly by hand the shell head should not jump past the tip of the stop).
If this is not the case, the front half of the stop can be adjusted (bent) to increase the engagement. Do this by removing the stop from the gun , and clamp the rear half in a vise, then bend the front in the direction of the curve in the front tip of the stop. Do not overadjust, it takes only a small amount to make a big difference. If overadjusted the ramp ingagement of the stop and its actuator ramp on the action slide bar will not mate properly. This can cause malfunctions and can damage the tips of the ramps.
If the shell stop is holding the shell in the magazine with good engagement, but will not release them during the feed cycle, then you must adjust the tip of the stop by removing just enough material from it to give clearance for the shell head to pass while the stop is pulled out of the way. Making sure that you have proper engagement of the ramps to provide the full movement of the the stops tip out of the way is important before you remove material from the tip. Again, this doesn't generaly take a lot of adjustment so remove only a small amount of material at a time using a file or dremel tool.
If you study the operation well before adjusting you should be able to tune this stop to the middle of it's proper travel and take away the possiblity of small variations in the diameter of the shells base causing a problem.
With the shell stop working properly there is seldom a problem with the interruptor. The tip of the interuptor has a less critical range of motion and is controled well by the pivot method. What the interruptor does is swing into position during the feed cycle before the first shell clears the magazine. By being in a position in front of the magazine opening at this time it prevents the second shell from being released during the action cycle. If it does not hold the second round from coming out of the magazine the result is a double feed jam. If it does not allow the first shell in the magazine past it to rest onto the shell stop, you will have complete failure to feed out of the magazine. Adjustments can be made to the tip of this stop by bending it in the direction needed to prevent the problems mentioned - it's just that this is a seldom seen problem.
So that's about it folks - I hope this helps somebody and questions/corrections are welcomed. Keep in mind also that these parts are not all that expensive and having a second set isn't a bad idea. Typically though, they don't wear out so to speak - they generaly are out of adjustment rather than worn out. A little tweak can make a big difference in reliability , and although this info is specific to the Mossberg, it can serve as a guide for many other brands of guns as well.