Huge trees occur throughout mythology. There’s the tree of life, and Yggdrasil, for example. There’s also the beanstalk that brought Jack into the land of the giant. In more recent history, Kaena and Ryzom come to mind. Any tree that’s big enough makes for a wonderful dungeon.
I first came across the concept in the old Das Schwarze Auge (The Dark Eye) adventure module Durch Das Tor der Welten – Through The Gateway of the Worlds – where (Spoiler alert!) the players are forced through the eponymous gate and end up on top of a huge tree. Their task is to get down safely.
In some ways, this sort of setting is a variation of the treetop village and, if your tree is large enough and/or features intelligent inhabitants, it might include a treetop village.
Due to the three dimensional nature of a huge tree, your dungeon map will be very different from a normal dungeon. Instead of having a floor plan, or try to map every little twig, a flow-chart like affair seems like the best approach. For each location, note what connections exist to other places. Make sure, in your description, to include what players see above and below them. How much is foliage blocking your protagonists’ sight?
Objective: The obvious goal of a giant tree is to climb to the top, or to get back to the ground. The Dark Eye adventure mentioned above used the later, but I personally feel that getting to the top is more intuitive. Obviously, you’ll need to make sure there are reasons for your heroes not to have access to flying machines, magic, or beasts. The reward at the top could be anything: A flying ship that got caught in the branches, or perhaps the tree pokes – much like Jack’s beanstalk – through a cloud and leads them to Serranian.
Climbing down would be more of a survival/escape story. Your characters start with limited resources and have to make do with what they can obtain during their descent. What brought them up in the first place depends very much on your setting. Perhaps they were jumping an air ship, or an annoyed dragon dumped them there instead of eating them.
Enemies: Anything you can imagine living in a tree. In the case of the singular huge tree, though, opponents could be a bit more faery-tale like. Flying beasts might perch on the branches. And if you are with Jack, a cloud giant could live above.
Special treasure: A seed from the tree may be very valuable to mages, alchemists, or as a curio.