Hi I was wondering if it is possible to connect to a computer that is on a "HOME NETWORK"?

Explenation: I built an IRC Program and i'm putting server on a computer that is on my home network.I go to www.cmyip.com and it gives me the internet ip of the computer but when i put it in on my client program i can't seem to connect.

If you don't understand here's what i mean.

1) Put Main Server on Computer that is on a home network
2) got Internet IP of the computer that is on a home network from (www.cmyip.com)
3) im at my friends house and i try connecting to the server with client program using the Same IP from (www.cmyip.com) but fails to connect.
4) i get extreamly pist off! lol

Don't worry i'm no noob so please don't ask me stupind questions for i'm used to working with networks.