The Long Answer
There are two pieces. For hardware, there is a Lilypad Arduino with a BLuetooth Mate Gold attached. This listens for and executes commands for how to control the four, multi-color LED lights. It's all powered by a Lithium polymer battery though I haven't done much testing, so I don't know how long it can go on one battery.
The logic for it all is running in a custom Android app on the Galaxy Nexus. Aside from handling the basic Bluetooth connection and providing basic manual controls of the hat, it starts a background service which connects to the Twitter Streaming API against a series of relevant hashtags. As the tweets come in, they are stored in local database, then parsed and if they contain a relevant word the appropriate command is sent to the hat.