SpeaknTweet is the first mobile Twitter client to use Google speech recognition. Google first launched search by voice about a year ago, enabling millions of users to speak to Google but also allowing some pretty decent speech recognition to occur. The combination of a powerful android device, an Internet connection, and datacenters in the cloud is what makes it work.
It's amazing stuff.
Speak 'n Tweet uses Google's Speach RecognizerIntent free form language model; the user's voice is streamed to Google's datacenters, utterances are converted into phonemes, then words, then phrases, then matched to Google's billions of daily queries to assign probability scores to all possible transcriptions.
This is all done in the time it takes to speak a few words. Pretty cool stuff.
Google folks describe the details here.