The option requires an end user to check an optional checkbox in the settings. The software doesn't require training done before use; rather it builds recognition over time. Here's what Google said:
If you opt into personalized recognition, we begin to associate the recordings of the words that you ask us to recognize with your Google account. We then automatically use these words to build a speech model specifically for you. This speech model enables us to deliver greater recognition accuracy. Although subtle, accuracy improvements begin fairly quickly and will build over time.If you want, you can opt-out of the setting later, and even disassociate the voice recordings from your Google Account, through the Google Dashboard in the Speech section.
Typical of many of Google's offerings for Android of late, the updated app requires Android 2.2 (Froyo) or higher to be used. You can find it in the Android Market.