Few notes to chip in:
DNS = Domain Name System, not Dynamic Name Server.
Also, it's not the case that the "DNS propagation" sends out the "bittybar.com = 123.123.123.123" to everyone, but rather it sends out "if you want to know the IP of bittybar.com, look at 12.12.12.12 or 23.23.23.23" - which lets you make changes at your DNS server and (depending upon caching) affect the world quickly.
Either way, DNS is a rather confusing subject - so if you've got any more questions, feel free to ask.
Note: If I made any mistakes about the innards of DNS, I'll feel like a real ass now, so I hope I didn't