A pivot point is the average of the previous period's high, low, and close. From that central pivot, three support levels (S1, S2, S3) and three resistance levels (R1, R2, R3) are derived formulaically. They are recalculated at the start of every trading day (or every session) and many intraday traders watch them as objective levels with no subjective interpretation.
Pivots work because they are widely watched — the level of order flow clustering around them is high enough to produce real reactions. They are most effective on instruments with strong session rhythm, like forex majors during the London–NY window and index futures.