Can you could try it again, and this time make a note of what happens (what you see with your eyes, don’t try to interpret) so we have a clue how to help you? You are our remote eyes and fingers. I suggest you try to push it into a forced reset (hard reboot) before you do anything else, because it’s a computer so in case of any doubt, reboot!
The forced reset is easy, press and hold both buttons (together, about 10 seconds) until the Apple logo appears, then release the buttons and let the watch restart. Then try the wipe procedure again.
If the two button reset hasn’t produced a response within about 20 seconds you might have a button problem, and you need hands-on help from Apple’s service techs. Contact Apple Support and arrange to get the watch examined at a Genius Bar appointment or ship to Apple’s service center.