Broadband is cable or DSL.
Narrowband is phone line.
With a broadband connection, people can "surf the web" faster, download things faster, and basically do everything faster.
So, it will allow you to play against more people online.
Narrowband does everything that the narrowband does, but slower, basically. This is why only a limited number of people can play online...
Hope that helps... and i hope that's right, too! lol.