These bands work according to the principles of Accupressure, which is derived from Accupuncture. For the alleged mechanism you can look up any source on those techniques, it is generally based on the concept of meridians and balancing ying, yang and qi. But I don't know of any explanation for these effects that I would call scientific.
I found a study called "Efficacy of Acupressure and Acustimulation Bands for the Prevention of Motion Sickness" which investigated two similar products: Acuband and ReliefBand.
The study used 77 subjects in 5 categories. They concluded
Neither band nor placebo prevented the development of motion sickness,
regardless of whether the bands were used correctly or incorrectly.
The study contains a rather uncritical description of accupressure, and the sample size is rather low, so I would not consider it very reliable.