You forward a port so other can contact your computer for the first time. In case of bittorrent you forward so others can connect to you, for example a seeder has a slot available and send a request so he can start seeding for you, if you don't forward the port the router will block the request, the same thing when you are seeding.
When you are surfing you are the one who is contacting the server for the first time so the router won't block the web server response.
When you are surfing you are the one who is contacting the server for the first time so the router won't block the web server response.