It probably streams the audio over the data connection, either 3G or Wifi.

For any application using the 3G data connection, charges depend on if you have an unlimited data plan, pay per megabyte after a certain included amount of data, or pay per megabyte always. Log into "MyVerizon" (start at www.verizonwireless.com) and can pull up the plan details for your phone. You can check your month to date (MTD) utilization on that website too.

On your phone #DATA will tell you your 3G MTD usage via free text message and voice (at the same time more or less, the text arrives while the IVR is reading off your usage.)

Verizon is moving away from the unlimited 3G data plan, so if your phone is a recently acquired retail plan, likely you don't have unlimited data.

If you have a Wifi capable Blackberry and turn off your 3G radio, if the application still works, you shouldn't be charged at all. This would apply to hotspots at airports, home wifi, and Gogo on the aircraft, if their T&C's and firewall permit streaming audio this way.