The general mechanism of an air compressor is a piston or rotary element (e.g. rotary screw or vane) that draws in air flow, which is compressed right into a storage container. Naturally, because the piston or rotary element needs to move consistently and smoothly for this to function, it generally must be lubricated.
In a lubricated air compressor, there is lubricating oil which keeps the piston or rotary element running smoothly without damaging the mechanism. The lubricant also really helps to dissipate temperature and keep maintaining air compression efficiency.
Oil-free air compressors also use a piston or rotary element, but they get around the lubrication problem by coating the compression component with a pre-lubricating material like Teflon. Some oil-free compressors could also use water instead of essential oil for the lubricating and cooling process. These alternate materials 
Water Lubricated Air Compressor defend the pump and invite the mechanism to go smoothly without the need for any oil-based or synthetic lubrication.