Puppies, especially those who are very young, have to be carefully watched to make sure that they aren't developing any sicknesses or conditions before their immune system has grown strong enough to protect them. One major sign that something is wrong with your puppy is that its gums are white, or a pale gray color rather than a healthy pink. Regardless of the exact cause, if your puppy has white or pale gums it's a good idea to visit the veterinarian.
One of the biggest and most dangerous root causes of white or pale gums in puppies is anemia. The puppy's red blood cell count is down to the point that the pink color of the gums (which is caused by the flow of red blood through the tissue) is not only weak, but sometimes not in evidence at all. This could be because the puppy has a disease that's halting the creation of red blood cells, or because the puppy is not getting enough vitamins. This is a very dangerous situation and the dog should receive medical attention as soon as possible.
Another disorder that will cause the gums to appear pale (more of a grayish color than an actual white) is hypoglycemia. Translated into regular language, hypoglycemia is when there's a sudden and drastic drop in the puppy's blood sugar levels. This condition usually manifests sometime in the first 12 weeks, and it's more common in toy puppies than it is in larger breeds. Hypoglycemia may be brought on by the sudden growth spurts that puppies have, it may be an inherited condition, or it might be some combination thereof.
Another cause of pale or white gums in a puppy is parasites. These parasites can be internal (such as worms and intestinal parasites) or external (such as fleas and ticks). Regardless of where the parasites are located, if there are enough of them they could be bleeding your dog dry of his red blood cells. It's important that if you see fleas or ticks on your dog, or notice worms in its stool, that you take immediate action before the infestation becomes life threatening.