Maximum parsimony is the most popular method for reconstructing ancestral relationships.
In maximum parsimony, this criterion is the number of evolutionary changes that need to be postulated in order to explain the observed data with a given tree. The most parsimonious tree is the one with the minimum number of evolutionary changes. As an example consider the trees shown below. The tree on the left is the most parsimonious tree. The tree on the right is not as parsimonious.