All Laser Cutters need two additional devices which move air flow: blower which removes atmosphere / extracts smoke from machine and atmosphere compressor as a source for compressed atmosphere for so called atmosphere assist.
Why and How
Laser cuts by high temperature, very high temperature focused in tight beam. Side items of high heat are smoke and fire, both aren’t welcomed 
addition, smoke disperses laser reducint it’s efficienty and fire causes charring of materials / edges and will even get out of control causing serious emergency.
Fire needs surroundings to burn but it will also die if you blow too hard, think about a candle in the wind. This is essentialy what surroundings assist is normally for: compressed air flow is extruded directly at the laser head in a very tight stream and is directed at where laser touches material.
Pressure and volume of air
Pressure of surroundings is key variable for air support efficienty, in our shop we found out that optimal value is between 2 and 3.5 bar (31-50psi).
To accomplish required pressure compressor must push certain level of air through surroundings assist opening, specific volume depends on size of the starting and desired pressure. Top quality laser beam cutter heads have small and finely tuned openings while cheaper chinese cutters simply blow in general direction via huge holes.
Proper compressor
When choosing compressor you need to consider if it can constantly provide desired pressure and level of air. Small airbrush Air Compressor For Tire Production Equipment compressors little compressors boast amazing pressure figures but really poor flow rates enough only for airbrush pistols. Also if small compressor can push enough air it will likely overheat in couple of minutes.