Just as with the Droid apps, when an untrusted certificate (Burp) shows up for an app requiring SSL/TLS, the app crashes and burns. The best way (same as Droid) to fix this is to import Burp as a trusted Certificate Authority (CA).
Why would we want to do this? Apps on mobile phones are cool but some would argue the web-services the apps are communicating with can be even juicier. We'd like to intercept the communication to the web-services and play around a bit.
You'll need to export the Burp Certificate, I usually open Firefox, set the browser to run thru Burp, view the certificate, export the certificate. Much like this.........
Browse to https://twitter.com (while proxying thru Burp)
Select PortSwigger's cert
Save Certificate with a .cer extension (.cer is what the iPhone recognizes)
Start a web server to host the PortSwiggerCA.cer
Browse to the location of the PortSwigger.cer file
The iPhone detects .cer, asks you to install as a CA, do it :-)
WiFi configuration, click the blue arrow on the right of your network
Configure with Burp's IP & Proxy
Hopefully that was easy enough to follow along. Now you can proxy your iPhone apps thru Burp.