The act of hitting all the requisite balls during a billiards game in one turn to win.
Doing it on one's first turn on the table is to doing it any other time in the game is as getting a royal flush is to getting a straight flush in poker.
To keep winning a game (beirut, beer pong, pool/billiards, checkers) so that you stay on the table and opponents keep coming like lambs to the slaughter.
When you (and possibly a partner) simply cannot be beat in the game of beer pong. Typically this is only acknowledged after 5+ games have been played (in a row) and won.
Guy #1: "Dude, have you seen Darrell and Ty tonight?
Guy #2: "Hell ya man! They are definitely running the table!"
By Adan
Running The Table
Relating to billiards: Taking the break, then proceeding to pocket every ball thereafter without miss or scratch.
This saying comes from playing pool. It means to sink all of the balls on the table, not giving the competing party a chance to even shoot. In pool if you sink a ball you get to shoot again and keep shooting until you miss. Only if you miss does the other party get to shoot and keep shooting until he misses.
It has moved to other areas meaning to win it all, for instance a team winning all of its games in a season.