A decision tree is a non-parametric supervised learning algorithm used for both classification and regression tasks in data mining. It has a hierarchical, tree structure consisting of a root node, branches, and leaf nodes. Each internal node represents a test on an attribute, and each branch represents the outcome of a test. The leaf nodes hold a class label, and the topmost node in the tree is the root node.

Decision tree learning employs a divide and conquer strategy by conducting a greedy search to identify the optimal split points within a tree. This process of splitting is then repeated in a top-down, recursive manner until all, or the majority of records have been classified under specific class labels. Whether or not all data points are classified as homogenous sets is largely dependent on the complexity of the decision tree.

Decision trees have several benefits, including little to no data preparation required, flexibility in handling various data types, and the ability to handle missing values. They are easy to comprehend, and the learning and classification steps of a decision tree are simple and fast. Decision trees can be used to solve both regression and classification problems.

In summary, a decision tree is a graphical representation of all the possible outcomes of a decision based on the input data. It is a powerful tool for modeling and predicting outcomes in a wide range of domains, including business, finance, healthcare, and more.