DCC
How DCC Chat Works
When you do a /dcc chat <nickname>, your IRC client opens a port on your local machine to listen for an incoming connection, and then sends a message to the other person to connect to your IP and the port you just opened.
Why you can't DCC Chat
Many computers, particularly home computers, are behind firewalls or NAT routers. These devices block incoming connections unless they are specifically configured to pass incoming traffic. We can't help you configure your client and router properly in this wiki (but Google can). If you can set up your client and firewall/NAT properly, you can DCC your Eggdrop. Can't do this? See the next section
How CTCP Chat Works
Eggdrop knows a lot of people aren't able to control their firewalls. Since Eggdrop's usuallly run on shells that aren't limited by firewalls or NATs, you can send a '/ctcp <nickname> chat' request. This tells Eggdrop to instead initiate a DCC chat request with you. Just like explained above, now Eggdrop is sending you the IP and port to connect to. Again, assuming Eggdrop is not behind a firewall or NAT, this should initiate a DCC connection between you and your Eggdrop