To decide whether to break a node into two or more sub-nodes, decision trees employ a variety of techniques. The homogeneity of the generated sub-nodes improves with the generation of sub-nodes. To put it another way, the purity of the node improves as the target variable grows.
ID3 stands for Iterative Dichotomiser 3, and it is so named because the method separates features into two or more groups iteratively (repeatedly) at each stage. ID3 is a top-down greedy way to building a decision tree that was invented by Ross Quinlan.