For \'ports to be open\' it means that people on the internet are able to connect to your IP address via a specific TCP port, whether this is to send you email, browse content on your webserver, download files from your ftp site, or whatever.
Firewalls block this behaviour as a security measure. ADSL and cable modems also block direct port access unless you tell it to \'forward\' these to your system via its internal IP address. This isnt a security measure as such, but is a symptom of Network Address Translation ( NAT ), in which your system has a different address to the one it uses to access the internet.
You will need to set up port forwards on your ADSL box if you are using one. Also enable access to bittorrent ports ( 6881, 6882, 6883 and higher, I believe each port is used to sustain 1 incoming connection for one in-progess download, enable incoming as well as outgoing traffic) if you are running firewall software. The details of how this is accomplished is specific to your setup, it may be time to read the manuals..
Bittorrent gives you faster access to a file if you are also uploading a lot, so the more people you let upload from you, the faster you will get through your download, as a general principle.