Pierced primer usually with an almost perfect plug knocked (burned) out of the primer. Some cartridges are more prone to it than others, but predominantly mentioned in competitive events. No hard and fast rules, but think very high pressure and large firing pin holes in breech faces. A very good example would be a 6.5×47 Lapua in a Remington 700 with standard firing pin. A "blanked primer" can wreck a finely tuned Jewell trigger.
I eventually sent every Remington 700 action I own (long and short), to Gre-Tan (Greg Tannel) to get his Firing Pin Bushing conversion done. Every other action I have is custom and have small diameter firing pins so it is a non issue, with one exception mentioned below.
Why some cartridges are more prone to it than others is a debate for those more expert than I, but if you see a pierced primer in say a factory 30-06, you have other issues like a sharp firing pin. A Surgeon short action I own was originally chambered in 308 and never had an issue. I had it rebarreled to 6×47 Lapua and couldn't even get the load work up done until I had the firing pin bushed. The primer would flow into the firing pin hole and leave a nice tit on every primer. These were not hot loads.
The family of cases I referred to above would be have one trait in my experience. Lapua brass, small flash hole, small rifle primer. Oh, and there are no downsides to a small diameter firing pin and corresponding small firing pin hole.
Out of curiosity, what is this new to you cartridge you are speaking/typing of?