Every webpage (unless it is really old and poorly built) contains all kinds of embedded links, images, scripts and other content. Every one of those embedded elements exists at its own URI. When you open a web page, your browser gets the contents of the page, which includes all those embedded element URIs - which means that the browser then has to go and fetch each of them in order to be able to display them in the page when it is rendered in your web browser.
So yes, every time you open a web page, there will be a flurry of other connections - and the richer the content of the page you are loading, the more additional connections will be required to get all of its content.
Now I've never used Norton, so I can't really comment on it except to say that it appears to have a well-earned low reputation vis-a-vis Macs...but regardless of what security tools (if any) you use, trying to monitor HTTP connections while you are actively web browsing is going to be a collosal waste to time.