A model that works by asking a series of yes or no questions, like a flowchart. Is the customer over sixty? Have they claimed before? Was the claim over five thousand pounds? Follow the branches to an answer. The appeal is that you can print one out and read it, which makes them popular wherever somebody has to justify the decision afterwards.
Technical view
Trees split the data recursively on whichever feature most reduces impurity, measured by Gini index or entropy for classification and by variance for regression. They handle mixed data types and non-linear relationships without preprocessing and need no feature scaling. Left unconstrained they overfit badly, effectively memorising the training set, so depth limits and pruning are essential. A single tree is also unstable: small changes to the data produce a very different tree, which is precisely the weakness that ensembles turn into a strength.
Related
Part of AI Terminology Index, section: Classical Machine Learning.