Like father like son:
The Spanish expression refers to the similarities between fathers / parents and sons and particularly at the heredity.
A palo is a stick (a piece of wood) usually cylindrical in shape and a chip is one of those small pieces emerging from the timber when it is cut with an ax, saw, etc. Normally the chip will be one way or another (color, texture, etc..) depending upon the wood (or bat) which is removed.
Well, using a metaphor, one could consider that parents are the stick and the children the chip, and therefore as the parents, so are the children.
But not always is the case but for where those who do, it is used this expression. For the other cases we have expression like be the black sheep.
For example, a boy who becomes a great doctor like his father. Well it is normal that your people around you say, if clear, like father, like son.
It is also used in the case where the resemblance is bad.