Pivot Points are calculated Price Levels that the day traders like to watch during the trading session.
In general, if the day's Price Action starts above the "Pivot", it will tend to stay above the Pivot (also called the "fulcrum" of the day's activity). On such a day, Resistance will be met at Price Level R1. Should R1 be broken, further Resistance will be expected at R2.
The story is all reversed, of course, if the price action is below the Pivot. Support will be met at Price Level S1. Should S1 be broken, further Support will be expected at S2. If, after starting the day above the Pivot, the Price crosses back through the Pivot, the Pivot will act as a Resistance area.
Pivot Points and Levels are Support and Resistance levels, and behave exactly like any historical Support and Resistance level.