Google's service for Indic languages was previously available as an online text editor, named Google Indic Transliteration. Other language transliteration capabilities were added (beyond just Indic languages) and it was renamed simply Google transliteration. Later on, because of its steady rise in popularity, it was released as Google Transliteration IME for offline use in December 2009.
It works on a dictionary-based phonetic transliteration approach, which means that whatever you type in Latin characters, it matches the characters with its dictionary and transliterates them. It also gives suggestions for matching words.