MapleBit is a terrible example of good PHP. The way it was written is very outdated, and you absolutely should not use it to learn PHP. Definitely look into the link posted in the above comment, and also look into Symfony Components, and the Laravel framework. Also, reading up on PHP PSRs, MVC paradigm, and other general programming concepts (OOP) will be helpful.
VBulletin (and most frameworks) use something called MVC, which essentially splits the logic (backend PHP code) from the presentation (HTML/CSS/etc). Thr brackets you see {likeThis} are part of the VBulletin template system. For something similar, look into Mustache.
Finally, MVC is just one of many paradigms out there. Something that is becoming increasingly popular is the idea of building an API and client to consume the API instead of building an "all in one" web app. This separates the logic and presentation further, making cross platform development faster.