Very young animals are highly susceptible to infectious disease because their immune system is not yet fully mature. They receive protection through antibodies in their mother's milk. Still, the protection is not long-lasting, and there may be gaps in protection as the milk antibodies decrease and their immune system is still maturing. Maternal antibodies can also interfere with a puppy's or kitten's vaccine response, so a series of vaccines is typically recommended to ensure that the puppy or kitten receives a vaccine as early as possible after maternal antibodies subside.
In many instances, the first dose of a vaccine primes the immune system against the virus or bacteria, while subsequent doses help further stimulate the immune system to produce the important antibodies needed for long-term protection.
An incomplete series of vaccinations may lead to incomplete protection, making puppies and kittens vulnerable to infection.
A series of vaccinations are scheduled to provide optimal protection against disease in the first few months of life, usually 3-4 weeks apart. For most puppies and kittens, the final vaccination in the series is administered at about 4 months of age; however, your veterinarian may alter the schedule based on your pet's individual risk factors.

The above information was obtained from the AVMA Vaccination Resources Tool