First off you'll want to know the rule. Basically it limits the highest gear a Junior can use in a race. The specifics sit in the USA Cycling (USAC) rule book, currently on their site here. In the first section, on page 50, you'll see the rule regarding the gear limit, with the actual limits on page 51.
The gear limit is a roll out of 7.93 meters, or about a 52x14. Since a huge tire will increase rollout there's only one way to check to see if your 52x14 is legal - do a roll out. In the old days the limit for the oldest Juniors was a 53x15 or a 7.47 meter rollout, and younger Juniors had to use a 53x16 or even a 53x17, depending on the age. Now it's a straight 52x14 for all ages.
To do a roll out you should mark off a length of hard surface 7.93 meters long, or 793 cm. You can mark this in the garage, on your driveway, maybe a sidewalk, but I would highly recommend not scratching marks in the hardwood floor in the living room.
Next put the bike in the biggest gear, the 52x14. Make sure the tires are reasonably inflated, i.e. they support the weight of the bike without deforming. Roll out is done without the rider on the bike so you don't need to weight the bike to compress the tires (which you want to do if you're calibrating your cyclometer).
Finally line up the crank on the first mark, pointing it straight down. Then roll the bike back in a straight line to the second mark. The crank should finish one revolution as you get to the mark. If it hasn't then you're over geared, usually because you have a huge tire on your wheel.
Remember there is no excuse for failing rollout! If you fit a 38c tire in your frame and you have a 52x14 you're going to fail rollout. You cannot use the "but I have a 52x14!" excuse. If the cranks don't do one revolution in your biggest gear in 7.93 meters you fail. You can always go shorter, like a 51x14, but there's no advantage to doing that.
Okay so that's the rollout rule. Why the heck is this rule in place? Why make racing even more difficult for Juniors to get into?
The main reason for the gear limit is the different levels of physical development in the under-18 set. A rider yet to go through puberty may be lining up against a rider that shaves daily. As an example when I first started racing I weighed in the 90 lbs range and I didn't have to shave. I would line up against guys who had 5 o'clock shadows and probably weighed close to 180 lbs. Two riders of different physical maturity levels will have dramatically different levels of absolute strength. Gear limits help (just help) level the playing field by reducing the impact of leg power.
Nowadays kids hit puberty a bit earlier than before. The gear limit is higher than it used to be, in reflection of that.
The gear limit, by reducing "top speed" (at least on the flats), reduces the effectiveness of aero equipment. Although not a huge thing it prevents physically mature riders from smashing the 53x11 at 38 mph on the straights. Using a 52x14 should allow most riders to finish a somewhat competitive flat race.
In this race I'm limited to a 39x11, the equivalent of a 53x15.
I didn't make the break or the chase but I won a lightly contested field sprint.
Finally a smaller top gear forces the rider to spin, teaching them good pedaling habits. If you see a Senior (i.e. 18 years old or over) rider who pedals very fluidly, they either worked on it consciously or they grew up racing Juniors. There are not that many Senior riders with pedaling deficiencies that consider working on pedal stroke to be an effective use of their time. As a Junior you have no choice.
Let me point something out - I don't recall seeing, in umpteen years of racing, a Junior that pedaled poorly. Senior riders, yes, all the time, and Masters, definitely, but Juniors? No.
I even note that my pedaling improves in the clip above.
Incidentally, after getting my butt kicked for 3 years as a Junior, my first Senior race I won every prime and won the race. The next Senior race I worked for a Senior teammate, leading him out to a win. The next Senior raced was a 6 sprint points race. I won the first two sprints, got 3rd in the next (caught a 4 lap break on the line but they got 1st and 2nd), then won the next 3 sprints. I mixed up my tactics, doing short sprints, long sprints, doing a full lap solo, starting the sprint from 20 riders back, getting led out, leading it out, etc. Yes, I used bigger gears, but I used what I learned about bike racing, partially because of the limitations imposed on me by Junior gearing.
I think that Cat 5s should also have gear limits. It's not just for developing knees, it's for developing racers.