Ok, basicly were dealing with two networks here, the internet and your local network. Comcast or any other service provider assigns you a INTERNET IP address, which points all internet traffic to your router. This may be static (always the same, most common for buisnesses) or dynamic (changes every few days/weeks, most common overall).
Now when you have a router you have your own local network, which consists of the router and one or more computers attached to it. The router opperates a DHCP server which assigns a LOCAL IP to each computer on the network. This IP may also be static or dynamic.
Local IP addresses almost always start out with 192.168.*.* with the most common defaults being 192.168.0.* and 192.168.1.* An example would be your router address may be 192.168.0.1 (almost always ending in 1) and your computer addresses may be 192.168.0.101, 192.168.0.102 etc.
Now, in this situation when you connect to bittorrent your internet IP address is known to every client on the torrent, as well as what port you want to listen on. So someones client will send you traffic to your internet IP at that port example 188.8.131.52:47251. Your router will recieve this and if you don't have port forwarding set up will ignore the traffic. But say if you have port 47251 forwarded to a local address ex 192.168.0.101. The router will know to send that traffic directly to that computer.
Changing your local IP to be static is very easy and defintatly free, static Internet IPs cost money(you can run a file/web server with them) Why you need your local IP to be static is that dynamic IPs expire and are renewed at not always the same address. So one week your computer may be at 192.168.0.101 and next week its at 192.168.0.103 and your router will be forwarding the traffic to the wrong computer.
There are many portforwarding tutorials out there, check out portforward.com
If you have a firewall program in addition to your router,such as windows firewall with XP sp2 or any other personal firewall, you need to open your listening port on that program as well to prevent the traffic from getting stopped once it reaches your computer.
Hope this helps, remember when you download torrents leave your client running for a while after your done so other people can download the file ( Seed! )