A firearm locking mechanism that is integrated into the firearm's frame and requires a key to unlock. They are typically found in revolvers, like some models made by Smith & Wesson and Taurus. They can also be found in semi-auto handguns, like some models made by Bersa.
The "Hole" refers to the hole in the firearm's frame that the key is inserted into. "Hillary" is a reference to Hillary Clinton, a politician with a pro-gun-control stance.
Hillary Holes are widely derided by firearms enthusiasts. The lock is deemed to be unnecessary and a potential source of mechanical failure. The hole for the key is also widely considered aesthetically unpleasing.
"I won't buy any Smith & Wesson revolver with a Hillary Hole. What an way to ruin an otherwise gorgeous handgun!"