Hearthstone has a slew of combinations you can use and the perfect chain of cards can eliminate your opponent in an instant...but I do not think they had this in mind. User Mamytwink created a combination that not only took hours, but days:
Kotaku was kind enough to inform how such a breakdown is possible: 
"The short version? Mamytwink has seven Prophet Velens in play, each of which double the number of arcane missiles he, as a mage, fires. He's buffed each Velen with numerous other cards to boost damage even further. To set things in motion, he played nine arcane missile cards in this one turn, which—thanks to all the Prophet Velens and their buffs—comes out to 28,752 missiles (258,768 points of damage). If Mamytwink's math is correct, it should take somewhere in the ballpark of 43 hours for the animation of all those missiles firing to complete."
The opponent is sitting pretty with Ice Block, which explains why they have not died immediately, as that ability describes: "When your hero takes fatal damage, prevent it and become immune this turn".
An interesting chain of events for sure, you can watch the feed live at his official Twitch site - http://www.twitch.tv/mamytwink
 - Kotaku - Hearthstone Player is Six Hours Into Attempt at Longest Turn Ever - http://kotaku.com/hearthstone-player-is-six-hours-into-attempt-at-longest-1693126341