Decision trees are one of the most widely used and practical forms of machine learning and data mining. They have been widely researched and applied to a large variety of data mining problems. (Decision trees are also known as Classification Trees or Regression Trees based on whether the classification is being done on real values or on categorical variables.)
Decision Tree: Forecasting whether Golf will be played based on the Weather condition

Trees are used to predict the membership of new cases into existing classes based on some information. As an example, the classification of a new loan applicant into risk-based categories can give a bank an idea of how the applicant is likely to perform on his/her loan. The bank can use this information to approve/reject the loan, and/or to price the loan based on risk. (Riskier applicants get more expensive loans).

A simple Decision Tree to predict attendance at a Golf CLub based on the weather can be found at Wikipedia::Decision Trees

Decision tree models are built by a process that is known as recursive partitioning. Click here for a more detailed explanation of the process.