Voxophones are the BioShock's version of audio logs you may know from many other games and their role is to provide story background and to fill the gaps left in the main campaign. These journals are a hot commodity in BioShock: Infinite, because they answers a lot of questions needed to fully understand the ending of the game. You'll find 80 Voxophones over the course of the singleplayer mode and collecting them all is required to unlock the Eavesdropper achievement/trophy.
There's also an additional Voxophone that for unknown reasons never made it to the final version of the game. Its transcription can be seen below.
Voxophone #?? - Good Genes Rant - Jimmy Jampot
"How is it that we of Columbia are so careful with the pedigree of our dogs and horses and then leave the ancestry of our children to blind sentiment? A lovely young woman could be riddled to the core with feeble genetic code. Here genes could breed criminals, paupers, and bedlamites if not rooted out of the genetic pool! Citizens should not choose mates for themselves!"