Git uses the Myers Diff Algorithm. This is a link to the original paper. Here is a Python code and interactive visualization from the Robert Elder's Blog. James Coglan also has a series of articles in his blog about it. Here is a table of contents of the series:

• Building Git by James Coglan
  • The Myers diff algorithm
    • Part 1
    • Part 2
    • Part 3
  • Myers diff in linear space
    • Part 1: Theory
    • Part 2: Implementation
  • Merging with diff3
  • Why merges fail and what can be done about it
  • The patience diff algorithm
  • Implementing patience diff