When you drift off, you fall asleep gradually and peacefully. If you woke up early this morning, you may drift off as you lounge on the couch watching TV tonight.
To drift off is to be taken and carried into sleep, the way a boat might drift away on the water. Like other phrases formed with drift, including drift apart, this one implies passive rather than deliberate movement. You may find yourself starting to drift off while you sit through a boring lecture, or when you're extremely sleepy, as your head first hits the pillow in your bed at night.