The springy pads used under carpets and rugs are called linings. Their most important purpose is to increase the life of your floor covering by decreasing the friction between it and the hard floor.
More than that, they add appreciably to the feeling of softness underfoot. They provide additional insulation, conserving heat and deadening sound.
They minimize the irregularities of an uneven wood or concrete floor.
The best carpet linings are made of cow hair, which is durable and very resilient, the second best of combinations of hair and jute, and the least desirable of jute alone.
The hair and jute is punched or pressed into both sides of a burlap foundation. The "waffle" surface (little raised squares on one side) is placed to the floor, creating a certain amount of suction which prevents slipping.