There are two types of hernias that are relatively common in puppies, inguinal and umbilical. Although neither has any long tem effect on health, we will absolutely notify you if we know your puppy has a hernia before they go home.
The first type of hernia is an inguinal hernia. They are generally considered to be genetic and are less common than the other type of puppy hernia, but easier to miss. We have never dealt with an inguinal hernia in one of our puppies at the time that I am writing this. What you will see is a "bubble" near where the belly meets the inner thigh. This does need to be fixed, and, unless your vet recommends otherwise due to unusual circumstances, can generally be done at the same time as spay or neuter.
Umbilical hernias are more common, and do happen on occasion. An umbilical hernia is caused by a gap in the muscle at the belly button that allows a bit of fat to pop through under the skin, creating a small bubble on the belly. In some cases, they can have a genetic pattern, but often it comes from Mom cleaning a little vigorously or pulling when she removes the placenta from pup at birth. An umbilical hernia does not have any long term health implications whatsoever as long as it is fixed. The concern with an umbilical hernia, if it isn't fixed, is that something more than just fatty tissue (intestine, for example) can possibly come through and cause a dangerous pinch. This is not at all common, but does make a hernia worth fixing.
Although you should visit with your vet about it at your puppy's first appointment, you can know that there are two ways of "fixing" an umbilical hernia.
1. It is very possible for an umbilical hernia to repair itself as the muscle strengthens. If a puppy you bring home has an umbilical hernia, it is an excellent practice to massage it back in every chance you get. Over time, you may notice that it is more and more common to find that it hasn't popped back out-----this gives the muscle time to heal together and strengthen to keep the tissue inside for good.
2. If your puppy's hernia has not healed on it's own by the time of spay or neuter, the general recommendation would be to have the hernia repaired in the same surgery. It is a very quick addition, and only adds minutes to the procedure. Healing is simply a few stitches, and most vets use a variety that will disappear on their own and don't even require a second visit. Some vets do offer to repair the hernia right away, prior to the time that you wish to spay or neuter your pup (read here for why delaying spaying or neutering is something to think about!), however, unless the hernia is an unusually large one or one that your vet thinks may cause issue for whatever reason, the risk associated with a second procedure is considered to be worse than that of actually having an issue with the hernia. Again, something to visit with you vet about, but we recommend to our families that (unless there is an unusual circumstance) the hernia repair be completed at the time of spay or netuer.