The "airs" are solo songs. According to Anthony à Wood, the college at Oxford University were very impressed with his book.
It has 240 completely scored songs, mostly airs, representing the works of Henry Lawes, William Lawes, John Wilson, and John Gamble himself (28 songs), among others. The book was probably compiled, as the flyleaf note says, in 1659 ("anent" for "ament" and an his genitive for "Gamble's").