The air compressor hose is what connect your compressor to the working air tools. Usually, the hose will be included when you purchase your new air compressor. However, as time goes by, you may want to upgrade or replace your hose, as it wears down due to a long period of usage.
For non-commercial air tools, you just need a hose between 0.25 inch to 1 inch. Also take a reference from your instruction booklet, as the air compressor hose size is indicated in there. Usually, a rubber hose is common and easily found, but do consider PVC hose as well.
One rule of thumb to live by is that the higher the air volume required from the air tools, the larger the hose line necessary to maintain. If the hose is wider, there will be more air flowing through at a certain pressure point. So if your air compressor operates at a very long distance from the plug, the larger hose size will benefit a lot, as constant air flow is better guaranteed with stronger material.