It’s normal for most double-headed drums to have a small hole (maybe 3/8” or 10mm) drilled through the side of the shell to allow the escape of air. When the drum is struck the batter head is depressed and air is forced out through the hole.
The hole is often disguised within the company’s badge, the plate being held in place by a grommet that is fixed into the air hole. In some older shells, like Gretsch round badge drums from the 1950s, there was no air hole. Striking the drum increases the pressure inside the shell and elevates the tone and slightly compresses it.
Since these Gretsches were closely associated with bebop jazz and bebop drummers tuned their drums high and played fast and light, this suited the drums. It may indeed be part of eThat Great Gretsch Sound’. With today’s harder hitters, air holes are generally considered necessary. In fact some drums have several holes. Yamaha’s Birch Absolute bass drums have four extra holes. The extra holes are even more useful now that so many drummers are returning to bass drums with no porthole in the front head.