ASME is the acronym for the American Society of Manufacturing Engineers.
This association has, among other things, been involved with the testing and certifying of air tanks. This can be important as it pertains to compressor receivers.
When you purchase a compressor from a reliable source, it's a safe bet that the tank is approved by a certifying body to provide the application safety it needs.
If you purchase an air tank / receiver separately from your air compressor system, you want to ensure that it has some safety or structural certification, and an A.S.M.E. stamp is one of those.
Usually there will either be a stamp embossed right into the tank metal, or there will be a plate riveted on the tank with the specifications and approval(s) numbers.
You should look for this when buying any tank for compressed air.
If you would like more information about A.S.M.E., please visit their site at: www.asme.org.