Original iPad Air
To be clear, this doesn’t refer to all iPad Air models, only the original iPad Air, which won’t be compatible with iOS 13. This original version came out back in 2013 and is quite old by now: The iPad Air 2, which came out in fall 2014, will be compatible with iOS 13. This is also true for all later iPad models, which include the iPad 5th-gen, and both the 9.7-inch iPad Pro and 10.5-inch iPad Pro (as well as larger, later models).
The terminology here is particularly confusing, but bottom line: If you bought an iPad before 2014, it won’t be able to run iOS 13.