It’s whatever nickname the person is using.
It’s the name set in your client. If there’s a leading tilde (~), the client is not running identd.
It’s the masked hostname of your connection. Your unmasked hostname is never publicly available.
You may have noticed that some people have vhosts, a virtual hostname, which hide their real connection’s name. On the GeekShed network, you can be assigned a vhost if you donate to the site or if you have been registered for 90 days or longer. If LordBaconCheeseburger donated $5 to the network, for example, his hostmask could change to LordBaconCheeseburger!~TFlash@nickel.supporter.geekshed.net. If someone has a vhost, you can still see the person’s actual hostmask with the command, /userip <nick>.