Leeroy Jenkins is a lvl 60 paladin in the game World of Warcraft.
He's in a guild called Pals For Life on the server Laughing Skull.
In the video that was not made by him, rather a guild mate he shows frustration over the tedious speeches his guildmates are giving to kill the dragons in the next room.
In WoW some rooms are very difficult to kill things in and in the room they were going to enter (the Rookery of Upper Blackrock Spire) there are a bunch of still dragon eggs. If u touch an egg it hatches a dragon that ends up touching more eggs hatching more dragons and thus creating a lot of chaos very fast.
His guild mates are spending a lot of time trying to go over their strategy and Leeroy who is off getting chicken out of his fridge is not paying attention. When he comes back the maker of the video silently orders him to run into the room. Leeroy complies and ends up hatching almost the whole room and dragging all of the pissed off dragons back to his friends.
Needless to say everyone dies.
The most funny things about this video is that the room itself is actually very easy to do. The dragons that spawn hit very hard, but are very easy to kill meaning that there will never be more than 4 hatched at one time, unless you screw-up major like Leeroy. Also the strategy that the guildmates are going over is incredibly stupid. Everything they intend to do are the most basic things you should NEVER do in the Rookery. The most appealing thing though is the dialouge that you hear over the game. Leeroy upon entering the room lets out a hilarious cry of his own name stretching it out for like 30 seconds.
This gave rise to the popular LLLLLLLLLLLEEEEEEEERRRRRRROOOOOOOYYYYYY JJJJJJJJJJEEEEENNNNNNNNNNKKKKKKKKKKKIIIIIIIIIIIIINNNNNNNNNNNNNSSSS cry before someone would intentionally kill their friends to be funny.
Leroy Jenkins who the WoW character is named after is a popular African American Jazz artist who himself enjoys the video, although he has no direct relationship to the character or person who plays the character.
The Leeroy Jenkins Video is incredibly popular and has been used in various commercials and TV shows such as Jeapordy.