Each operation is given a score (weight), usually, insert and delete (indel) operations are given the same score, and using alignment algorithms, we search for the minimal scoring (or the maximum negative scoring), representing the minimal number of edit operations.
Since most of the changes to a DNA during evolution are due to the three common local mutations: insertion, deletion and substitution, the edit distance can be used as a way to roughly measure the number of DNA replications that occurred between two DNA sequences.