What does "like father, like son" mean?

In the same manner from generation to generation, as in Kevin decided to run for mayor—like father, like son. This ancient proverb has been stated in English in slightly varying versions since the 1300s, sometimes appearing with a counterpart, like mother, like daughter. Thomas Draxe had it in Bibliotheca (1616): “Like father, like son; like mother, like daughter.” Also see chip off the old block; follow in someone's footsteps.