This was possible before TestFlight rolled out a service. The technique stemmed out of the enterprise distribution mechanism. Since 4.0 devices have supported install from web.
Remember - you still need to sign the beta distribution for a select set of UDIDs you can't just willy nilly install it on any device. All they are doing is taking the email the IPA step out of things.
Update: I want to say that Test Flight is one of the most helpful tools I've used when developing though. Just taking the IPA emailing out of the picture was an understatement- I was just trying to call out the technical mechanism. They do a fantastic job managing the whole beta process. Getting new devices enrolled. Notifying users etc.
Stock iOS devices are "vulnerable" to running the user loading Ad Hoc apps from any developer who has that device's UDID, and registers that UDID among their 100 allowed devices on Apple's developer portal.
OTA distribution is just another way to install an Ad Hoc beta test distribution from an enrolled developer.
Yes this is a core feature of iOS for Enterprise Customers who wish to distribute OTA.
Presumably you would pass your UDID over to TestFlight along with the app and they use their Enterprise Licence to send the app to you. I'm sure I'm missing a lot of the technical details but if you want to know more, Apple has a video on this from WWDC 2010.
Login to developer.apple.com, go to WWDC 2010 Videos and use the link to get to the vidoes. The video you want is "Session 108 - Managing Mobile Devices". It is very informative about what is possible with OTA and the steps you have to take to do OTA provisioning.
This article showed how Apples OTA implementation works and can be used outside enterprises as well: ios wireless app distribution
The complete process is documented by Apple.
Apple also published documentation and sample code for registering devices and get the UDID by using profiles, so your website can detect which device is calling.
Some additional solutions with different strenghts:
iOS Beta Builder, a Mac Application to create the website by using a build. Simply upload the resulting files to your webserver.
Diawi: Simple Web service. Upload your IPA file, optionally set a password and send a link to your testers.
AppSendr: Web service for beta build hosting, similar to Testflight, but does not include the device registration process. But provides deployment utilities to automatically upload new versions.
HockeyKit: Open source project for hosting beta versions on your own PHP5 server with additional functionalities like an client for In-App-Updates, automatic device specific web sites and handling multiple applications. Completely file and directory based.
HockeyApp: Web Service for beta build hosting, In-App-Updates, Statistics, and including device registration, invite and recruitment. Also provides server side crash report collection, symbolication (for all threads) and crash grouping for beta and app store apps (iOS + Mac). SDKs are open source, using HockeyKit, QuincyKit and PLCrashReporter (which is the only safe solution on how to do crash report collection on iOS, see this article.
Testflight basically uses the normal Ad Hoc as already stated.
For this to work, you need the UDID for every device in order to add it to the Ad Hoc profile, re-compile the app with the new profile an redistribute the new build.
You can get the UDID with the help of the OTA Authentication Request. This is actually a step that is done in MDM before the actual profile is rolled out to the device. It basically asks the device for further information about itself and send it back to a self specified server.