While a normal tire is designed to deform in shape either from leaning the bike during maneuvering or cornering, the tire can be deformed to such a point where the likelihood of it separating from the rim is possible. This unintended separation of the tire from the rim is known as "roll-off" and is catastrophic to the rider because of the sudden loss of traction and control.
Specially shaped material incorporated onto the internal side of the tire's lower sidewall allows the tire to compress normally under load, but beyond a certain threshold act as "bumpers" to prevent further compression - further compression that can cause the tire to roll off the rim.