A method of determining the cause of a problem.
Basically, you take every aspect of a problem, and run it through a process of elimination until you can locate the branch responsible.
For example, the NTSB investigates a plane crash by running the Fault Tree. There can be various causes that lead to a crash, so each one falls into a branch, such as Powerplant, Human error, Avionics, weather, etc. A small group is assigned to each branch, and they methodically check out any leads in their jurisdiction. Each group tries to determine a possible cause of the accident that falls in their department, such as a power failure or a wing strut cracking.
The people go through the procedures and eliminate every system on the plane as a cause of error. Through process of elimination the group can narrow down the fault to a certain branch and ultimately system. As you eliminate the irrelevant branches in the tree, you can narrow your focus and devote more time to the remaining solutions.
I use it as well when working. When I have the feeling I think something is missing in schoolwork, I run my own little tree. Methodically I go through the classes in order and one by one check for missing work. If I'm sure everything's done, I eliminate that class off my list and concentrate on the ones I'm unsure about or I know I have work due. Very efficient.