Sounds like he's describing the marine air as being crisp or cold. It should be "in the morning."

It means "sharpness". The edge of a cutting tool is sharp. Instead of "edge", you could also say "bite", "bitterness", "sting". Instead of "on the morning", say "In the morning the marine air had a cool edge to it" or do as C.M. suggests. "Marine air" is correct but not common. More common is "sea breeze".