Yes - Dragon Dictation is the 'standard' speech-to-text app and it's free. It uses the iPad's microphone but needs an Internet connection. I think that some of the processing is done away from the iPad. It does a reasonable job, but you do need to edit the file afterwards. It gets better with time, learning about your voice, so you need a little patience with it in the early days.
Like all speech-to-text programs, it can't cope with 'unusual' words, so it's not helpful if you're trying to dictate a scientific paper that contains a lot of technical terminology.
Tim
Scotland