Question About Firewalls and Hacking

Archived from groups: comp.security.firewalls (More info?)

Ok, so I read that having a firewall is good because it helps to prevent my
computer coming under attack by hackers and also helps block viruses and
worms from reaching my computer.

Question:
Surely if I drop my firewall my computer is only vulnerable if it has some
kind of trojan already installed on it that can respond to a connection
attempt?

If I have no such trojan and I tell the world my IP address and that I have
port 1000 open, how exactly can a hacker take advantage of that and 'attack'
my computer?

Thanks, Gaz.