Shiko is the sumo exercise most common to the layperson. Essentially it is an exercise to increase balance, strength, and dexterity in the lower body (essential to Sumo and ANY combat sport). Squats in general are often overlooked but essential to every body's fitness. Combined with lifting your leg, balancing, and setting down with control... shiko is actually quite challenging.
Readers of the Ground Never Misses will remember the excellent Sumo Documentary post a few days back with Hakuho taking about the fundamental importance of basic exercises such as shiko. He attributed this "old school" style of training to his success (arguably one of the best ever in professional Sumo).
Here is another great video of the science behind shiko: