Let's understand each operation: Insert: Add a character. "CAT" becomes "CART". Delete: Remove a character. "CART" becomes "CAT". Replace: Change one character. "CAT" becomes "CAR". Each operation costs 1.
This problem appears everywhere: spell checkers, DNA analysis, diff tools. For 'intention' and 'execution', the minimum edit distance is operations. Spell checkers use this to suggest the nearest matching word.