The inner liner is an rubber sheet compounded with additives that result in low air penetrability. The inner liner assures that the tyre will hold high-pressure air inside, without the air gradually diffusing through the rubber structure.
The inner liner replaces the need of an inner tube which was originally used to reduce air gradually diffusing through the rubber structure.
The removal of the inner tube normally decreases the amount of tyres that rapidly deflate when the tyre get an object pierce though it, this is because with a tube the valve is not sealed and air can be quickly escape from where the valve penetrates through the wheel. With a tubeless normally the only place the air can escape from is where the item has penetrated the tyre.