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Whenever you get high speed internet / broadband installed at a new location, the techs always pull up a speed test webpage to show you just how fast you're pulling data and sending data on your new service. The app SpeedTest for the iPhone does exactly this, but makes it a lot more reliable then wherever that tech is bringing you.
The app doesn't really have any bells and whistles. But it doesn't need to have any. It's a simple and straight forward app that just tests your network connection. The advantage is that you can try this over EDGE, 3G, and WiFi to check how fast you're sending and receiving. But when it comes down to it, you're still just pulling numbers.
The info you gain can't be saved or exported at all. You can of course screenshot it, but this isn't a bragging rights thing anyways. Don't be surprised when you actually pull down less then your service provider has promised, this is normal. And definitely don't expect them to care when you send in that screenshot.
SpeedTest is another app that any networking tech should have on their iPhone. For everyone else, it's not really important unless you're planning on shutting someone down on their claims of amazing WiFi connection to their network. Even then, it's probably not needed.