The type of mat you put between your platter and vinyl record has various degrees of importance depending on the material the platter itself is made of. Mats can be made out of a wide variety of materials including cork and leather, but the most common is a felt mat.
The mat itself has a variety of functions: it isolates, dampens, and can reduce static buildup. Without a mat, you could experience 'ringing' and other noise from the bearing and motor.
Some turntables don't require and hardly profit from mats though. This depends on the platter material. If your turntable platter is acrylic for instance, you don't require a mat. Still, some users enjoy them simply to spice up the look of their turntable.