Hi there and thanks for your question. What your vet is talking about is something called an umbilical hernia. This means that the body wall did not close completely at the location of the belly button.
In most dogs this is not a huge concern. There is often a tiny hole that a little bit of fat sticks out of. We usually repair these at the same time as doing a spay or neuter surgery. However, if the hole is large enough that intestines could poke out then this should be repaired right away.
The reason the vet says not to breed this dog is because this condition is genetic, so any pups that he produces are likely to have the same problem.
I hope this information helps! If you have more questions regarding this problem, just hit reply. Or, if my answer is sufficient, then please hit accept. Thanks!