Register this connection's addresses in DNS = let this workstation/server dynamically update,whatever DNS server it uses for resolution, with it's IP address. In other words, the machine boots with an IP address, and when the 2K OS loads, the machine sends an update packet to the local DNS server with it's configuration.
Use this connections DNS suffix in DNS registration = you have the ability to change the DNS suffix used by a network connection of any machine in your domain. Normally, you wouldn't do that, so the machine would register itself using your domain name as it's suffix. However, if you do change this, and you'd like the machine to show up in DNS with that suffix, this option allows for that.
Unchecking both of these options effectively disables Dynamic DNS registration. UNLESS, you use DHCP, and authorize the DHCP server to register connections for you.