In general there are three types of breeding, (and this is a very simplified description):
The first is called line-breeding, and is generally accepted to be the correct way to breed dogs, cats, and all types of livestock. With line-breeding, you breed dogs that are related, but not too closely. i.e. cousins
The theory with line-breeding, is that you will start to produce dogs with a predictable appearance to them. This way you can identify any problems that are appearing in the dogs you produce, (or lines), and can then try to correct those problems by out-crossing. Out-crossing is usually done after 2 - 3 generations of line-breeding. For example, I might be producing Mastiffs with great heads, but not very strong rear ends. I would then look for another line-bred line, (not related to my dogs), that produces very strong rear ends. Then, I would start line-breeding again, while retaining a strong rear end.
So, out-crossing is the second kind of breeding, and it is breeding completely unrelated dogs together. The problem with out-crossing, is that you lose any predictability in the pups. For example, as in the above, let's say I out-cross to a line-bred line to try and get good rear ends. I may not get those strong rear ends in the puppies at all! And could even pick up something I don't like from the line I just bred to - like eye problems. Out-crossing is an educated guess.
And the final type of breeding, is in-breeding. This is breeding closely related dogs together. Many breeders feel this type of breeding is perfectly fine. And breeders quite often disagree as to what, exactly constitutes in-breeding.
In my opinion, fathers/daughters; mothers/sons; brothers/sisters; and half-brothers/sisters are all in-breeding. In Mastiffs, there is a tendency to lose size when in-breeding. In all breeds, you can get some fantastic puppies when in-breeding, but you can also get some unfortunate results when in-breeding. Guess who gets those? Be very careful if you're being offered a deal for a puppy. As well, only very experienced breeders who have a thorough knowledge of their lines should attempt in-breeding. And it should only be done once - not repeatedly! What a recipe for disaster!
Successive in-breeding can result in poor immune systems; and all kinds of genetic defects. Why do you think it's illegal for humans to marry closely?
This has become the reason for all those weird breed crosses that have become so popular - supposed hybrid vigor in things like schnoodles; pugles; golden doodles, etc. This is not the case, but you do have to be aware of your pups pedigree, and avoid problems. Educate yourself!
Ask for a copy of the pedigree of the upcoming puppies, before putting down a deposit. If you don't know how to read a pedigree, then take it to your Vet, or the Vet you are planning on using when you get your puppy. They can advise you as to what sort of breeding your puppy is/will be the result of.
I like to point out that the wolf is a dog's closest ancestor, so I quite often look to them to direct me as to how I put my breeding program together and how I raise my dogs. One of the world's foremost authorities on wolves, L. David Mech, has indicated in his book, Behaviour, Ecology and Conservation, that it is rare for wolves to in-breed. There's got to be a reason for that! Nature has a way of weeding out the weak and unhealthy! So, I don't do it.