An accidental occurrence that can happen when skateboarding, especially during kickflips and heelflips. What happens is that while the board should do a full rotation along the lengthwise axis, it only does a quarter or three-fourths rotation, landing on the sides of its wheels.
Now, if you come flying down on top of the board in this position, expecting to land on nice, flat griptape, and instead land on a rather narrow (about 3/8 inch, .8 cm) edge of wood, you can hurt yourself. The least of your worries is that you could twist your ankle. If you did the trick from a good height, you could break an arm or leg.
Ex.- Dude, I landed primo on that kickflip and now my ankle is the size of a melon.
The origin goes back to the 80's. Freestyle skateboarding was still pretty hot, and you could make a living doing demonstrations around the country. Primo and Diane Desidiero did just that, as a husband and wife team. Their performance was pretty kitschy, and consisted largely of a synchronized routine. Primo far outshone his wife, but was limited to what he performed by her abilities. This all would have been just a footnote, but Primo had one signature move that he alone invented and performed. The Primo Slide.
A primo slide consisted of flipping the board onto the sides of its wheels and deck, standing on the other side's wheels, and scraping along the ground with your board on its side. It's a very difficult maneuver, and not many people do it today (though Rodney Mullen can be seen performing it in a few videos, including Globe's Opinion). Based on the slide, the very concept of the skateboard on its side was referred to as "primo". Since the move is performed so rarely today, the accidental primo is seen more often. And, of course, an accidental primo is far more likely to injure you.