PF Flyers are a brand of athletic shoes that are currently manufactured by New Balance. They were first produced by BF Goodrich in 1937. They had popularity in the 1950s and 1960s, but lost steam during the 1970s, 1980s, and 1990s. The brand was purchased by Converse in 1972, but later sold off due to antitrust issues. New Balance bought the rights to the brand in 2001 (which had been dormant since 1992) and resurrected it in 2003.
The style most commonly associated with the shoe is the common canvas-duck sneaker, with cloth reaching above the ankle, and a patch that reads "PF Flyers." This common style is called "Center Hi". They are very similar to the Chuck Taylor All-Stars manufactured by Converse.
Read more about PF Flyers: History