As the name suggests, tubeless bike tyres are pneumatic tyres with no inner tube. With traditional tyres, it is the inner tube that retains the air pressure, and it's this that you need to repair or replace in the event of a puncture. On both normal tyres and tubeless bike tyres, the tyre itself is held in place by its beaded edges connecting with the lips of the rim. The difference with tubeless bike tyres is that this forms an airtight seal.
Tubeless bike tyres can be more difficult to fit because the seal between rim and tyre needs to be extra tight. However, with proper preparation and care, fitting tubeless tyres should not be a problem.