"Live encryption", "on-the-fly encryption", "transparent encryption", "real-time encryption" are all different names for the same concept, used by SafeBit to give simplicity and efficiency to the encryption process.
When you open a file from the safe, the data is decrypted instantly. When you save it back, the file is re-encrypted automatically (on-the-fly). The user will not be aware of the mechanism behind it, that's why it's called transparent.
One of the major advantages that a live-encryption program has over a classic file encryption program is that you don't have to remember to re-encrypt the files you work with after you're done. SafeBit does this for you. Live-encryption programs are the next generation of encryption programs.