Whipping means hurrying production by killing population while running slavery. This is the most powerful form of production throughout most of the game. Failing to recognize the power of the whip is one of the main reasons why many players are stuck at noble or below.
Each population killed gives 30 hammers and each whip give one unhappy face for 10 turns. Most of the time 2 pop whips are best, this means killing 2 population for 60 hammers. To do this, the city must be between 31-60 hammers from completing a build. The excess hammers will be converted to overflow and put into the next build.
An example, you are building swordsmen, which cost 40 hammers each. Your city is size 6 and has 8 hammers invested into a sword. You 2 pop whip it for 60 hammers, which completes the sword with 28 overflow hammers. In addition you get the hammers worked by the remaining 4 pop in your city, which also will go as overflow into the next sword. So if you work 6 hammers, then the next turn the first sword is completed, and you will be one turn from completing the next. That's 2 swordsmen in 2 turns. Do this in 4 cities and you have 8 swordsmen in 2 turns. On Chieftain/Warlord, this is probably enough to kill several of your neighbors...