To explain decision trees, it's easiest to think of them as decision support system software (computer programs) that allow you to represent a decision graphically. You can represent different choice points, consequences, probabilities, costs and possible results.
Remember that they are rational decision making models and also visual decision tools.
They are rational because they're used to compare consequences and potential value of each of the decision making options in order to come up with the best possible alternative.
They are visual decision support systems in that they allow you to organise a lot of complex information graphically.
Decision trees are tree-like charts or diagrams used to represent a decision. Obviously included are the options that are available and for each option it may include many consequences, further decisions that may arise, the probability of its occurrence, the cost of, and the potential value as a result of choosing this option.
You start with the decision to be made and represent this with a box. Then branches are drawn, one for each possible option. At the end of the branch, will be another decision to be made, an uncertainty, or a result.
Typically decisions are represented by squares, uncertainties by circles and results by triangles. The squares and circles have more branches drawn until the ends of branches all lead to results.
Such information as value, possibilities, risks etc can be added. Decision Tree analysis is the studying of the information in order to choose the best option.
These tools allow for a visual representation of possible courses of action along with relevant factors to allow for an overall view of a potentially complex situation.
Decision trees and decision tree analysis are commonly used in computing in order to calculate probabilities and for data mining, and there is more and more decision tree software available nowadays.
In order to further explain these trees, it makes sense to have a look at some examples...