A private activity bond is defined by IRC 141(a): "the term "private activity bond" means any bond issued as part of an issue— (1) which meets— (A) the private business use test of paragraph (1) of subsection (b), and (B) the private security or payment test of paragraph (2) of subsection (b), or (2) which meets the private loan financing test of subsection (c)." It is a category of municipal bond, issued by a state or local government, and what sets it apart is who actually uses the money and who actually pays it back. When the answer to both is a private business rather than the public, the bond is a private activity bond, and the federal tax exemption that municipal bonds ordinarily enjoy is no longer automatic.
The section's title, "Private activity bond; qualified bond," names the two halves of the subject. The first half is the definition, a set of percentage tests. The second is the list of private activity bonds Congress has decided should keep their exemption anyway, because the private use serves a public purpose the tax law wants to subsidize: airports, low-income housing, student loans, small manufacturers, nonprofit hospitals and universities. The municipal bond page states the tax consequences in the course of explaining the exclusion's four holes; this page is about the definition, the tests, the qualified categories and the cap that limits them.