The "Normal Lookup Method" means that mIRC will find out your what's your IP address (and hostname) through your operating system. This means that you'll acquire the IP address known by your computer. If you're behind a NAT (or using a router), this is usually a bad idea, since the IP address seen by your computer won't match the IP address that other computers on the Internet (for example, an IRC server) are seeing you with when you communicate with them.
The "Server Lookup Method" means that mIRC will find out what's your IP address through the IRC server. Immediately after mIRC logs in to the IRC server, it'll send a command (USERHOST <your nickname>) as a way of asking the server what's your IP address (or hostname and then proceed to do a DNS lookup). This way, mIRC will acquire the IP address that other computers on the Internet are seeing you with.
Sometimes, even if you check both "Local Host" and "IP Address" for the "On connect, always get:" option, you'll only get your IP address (with an "unknown" host). This means that your IP address does not "translate" to a hostname with your DNS server. When this happens, you might also get a reply like "-server.network.org- *** Couldn't look up your hostname" when connecting; but, on rare occasions or if you have altered your hosts file, you will be able to see your hostname while the IRC server won't, and viceversa.
Also, it's impractical to get only your hostname, and this is why mIRC automatically checks "IP Address" in the "On connect, always get:" when you check "Local Host". Sometimes, while you are able to get a hostname through a DNS server, it's impossible to get back your IP address with that hostname through the same DNS server, which means that the hostname is an unreliable way of identifying you on the IRC network.
