I have an iPhone application that just shows a web page when you use it. I don't know the URL of the site it loads. Is there any way I can get the URL of the page the application loads?
To determine the web site, you will need to intercept the network traffic travelling between your iPhone and your Internet Service Provider (ISP).
A good proxy will offer log files and allow you to see server addresses and, if not encrypted, requested URLs.
Alternatively, you could contact the application developer and ask.
No, You can't get the URL of the loaded page until the developer of that application intended to show the url.
The other way to intercept the traffic apart from a proxy is to set up a sniffer, such as Wireshark.
Here are some instructions from stackoverflow.
If you prefer to use command line tools you could also use tcpdump, which is available from the OS X command line.
Another good proxy which I used to use in my work is paros, but it has now been superseeded by ZED attack proxy from OWASP.