The impression I get is that the base system is pretty simple, though it is wrapped up in elegant, if complicated, sub systems. The book explicitly suggests to play a session or two with only the first 80ish pages (The Hub, as it were), before adding in the other subsystems (the Spokes and Rim).
Whereas the games in the d20 family are fundamentally about the personal acquisition of power, the Burning Wheel system is about how a character's beliefs and goals move them to action. Gameplay focuses on testing and challenging the goals and beliefs of the characters. NPCs and events really should not exist unless they are able to challenge a character's convictions.
Character advancement primarily happens by both succeeding and failing tests, which means that characters need to keep challenging themselves in the areas that they wish to improve.
Character creation follows a lifepath system, whereby you choose different phases of your life, each of which will give you access to a different set of skills and resources. As a result, the system lends itself a little bit more to just following lifepaths and seeing what your character ends up as, rather than the more familiar case of having a specific character design in mind and then trying to recreate it as closely as possible given the character creation rules.
The setting of Burning Wheel isn't explicitly specified, though the included lifepaths do suggest a sort of Tolkien-esque fantasy world.
There is also the wonderful Mouse Guard RPG, which takes the Burning Wheel system, strips it down a little bit (e.g. one belief per character instead of three), adds a few things (primarily the concept of one's Nature - how 'mouse-like' each character is, and how that helps or hinders them in performing their duties, and the supplies a custom set of lifepaths in order to customize the game to the setting.
(Quick note: I may have got a few details mistaken, I'm writing this from sleep-deprived memory at the moment)
