The Hesitation was the second of the main Ragtime Waltz variations. The essential step was walking to the beat: three steps, then perhaps a half-pivot or some other movement to mark the end of the three-beat half-phrase. It often devolved into simply walking to the Waltz beat.
The first is a Swedish instructional film from 1915, demonstrating the proper execution of the Hesitation Waltz.
The second is people just walk-waltzing.