This phrase is used when a son is very like his father or (less frequently) when a daughter is like her mother. It's a fairly colloquial phrase and is used when there are similar characteristics involved. ie the father is a doctor and the son is studying to be one....the son is a chip off the old block. Or both have the same sense of humour, or follow the same sport etc etc
hope that helps,
To clarify the metaphor, if you have a large block of marble, and hit it so that a piece breaks off, the new piece (chip) is of exactly the same substance as the original, even if it is smaller and shaped differently. The child is the chip, the parent is the block, and they are essentially the same.
It is only an insult if the speaker lacks respect for the parent. However, even if it is intended as a compliment, it may make the child uncomfortable if he wants to be seen as completely different from the parent.