This refers to the body's basic need for insulin to keep itself in proper condition. A non-diabetic's pancreas produces this basal or "basic" insulin in sufficient quantities at all times. Insulin-dependent diabetics don't and they need to inject an intermediate or long lasting insulin 1-3 times a day to replace what their bodies lack.
Even if your pet is not eating, his or her body still requires some insulin; this need does not disappear because a dog or cat doesn't eat. (See the discussion at "Getting regulated-- feline diabetes". The advice regarding the need for a reduced insulin dose holds true for dogs as well.)
Intervet advises a basal dose of approximately 30% of normal insulin dose when a diabetic pet isn't eating. This should be discussed with your vet even if you do not need the information at present. Knowing what he or she considers to be your dog or cat's basal insulin dose should be noted in case of need.
Basal insulins are generally either the intermediate-acting or long-acting insulins. Most of us with diabetic pets are fortunate enough to have a basal insulin we give once or twice a day able to cover the pet's mealtimes as well. People are not so fortunate; they need to use a fast or rapid-acting bolus insulin to cover what they eat. Some pets, especially dogs, require this too.
Before there were insulin suspensions, there was no such thing as basal insulin. All of it was short-acting R/neutral type which made it necessary for those with diabetes to take many shots a day to maintain their blood glucose levels. Some people with diabetes refer to their basal as their "background" insulin. Another term for this type of insulin for this type of insulin is depot insulin.