Packet sniffing means intercepting network data. In the case of developing an application with Amfphp, it can be used to gather information about timing, or simply to look that the data that is being transfered is indeed what you expected. Some more advanced tools support reproducing requests and the like, and this can be used to test loading your server.
If your application runs on mobile, or anything else that isn’t your development computer, it is recommended to set things up so that traffic goes through your computer. You can do that either by simply using a mobile simulator, or if you must run on the mobile itself set things up so that your computer is a router and that your mobile’s traffic goes through it.
If your application runs in a browser, there are browser based tools that may be enough for your needs. Firebug includes some packet sniffing tools. There some included in Webkit based browsers such as Chrome and Safari.
If your application doesn’t run in a browser, then you should try a general purpose packet sniffer like wireshark.
These tools are all well and good, however they don’t understand AMF. If you want that, there are the following solutions: Charles Proxy, and Service Capture are general purpose packet sniffers. FlashFirebug is an addon to Firebug that will parse AMF.