How to monitor which apps are "calling home'?
For a fully featured application to monitor other applications' network usage (all traffic, not just http), try Little Snitch.

EDIT

Apologies, missed the whole key "app on my phone" bit. There is no way for one process to inspect or intercept data from any other app, since all apps are sandboxed. The only way to get close to accomplishing this is through a jailbreak.

Otherwise, you would have to enable logging on your router, and the specifics on how to do this or how easy it is depends on your firewall/modem/router. Little Snitch may still be able to help you here if you have your Mac act as the wireless access point.