I would like to add a page with its own content and assign a tab to it.
I was looking at adding extra TABS and creating a custom content page
You can achieve this in two ways, each requiring either an addon or a CMS app.
The addon is called Dahsboard Custom box, and I am currently using it with good success on two WBB installations. You can find the plugin here, but to download it you first need to register with that forum. Although the site is in German, the download link is easily found on the page. I have been using this addon since WBB 4.0, and I can confirm it works well with 4.1, too.
The other option is installing codeQuake Fireball CMS, which not only does it let to add tabs and insert texts, but it also allows you to create entirely new pages for your forum and insert whatever content you want in it. The app is still in beta (RC2 at the moment), but it already does a very decent job, and it's stable. Also, its learning curve isn't steep; you just need to spend some time familiarizing with the process of adding new content, but it's all pretty intuitive as you will see. I gave a very dumbed-down example here.
However, I think that we would all benefit from having a simple CMS integrated in core. It would be awesome if we could simply add new tabs and pages directly from the ACP without requiring external software. Including such option would make WBB even more appetizing.
While we wait until this will be included (hopefully), you can go around the problem with what I suggested above. Both ways allow you customize your forum as you like.