That is quite a big thing for your vet to say! If you are worried you should get a second opinion from another vet. But a lot of vaccination schedule planning depends on where you are located and what you are doing with your puppy. For example, my vet advised me to give my puppy a DH2PP vaccine every 2 weeks up to the 5 month mark. She got a LOT of vaccinations. I don't love that, but I have my reasons for my plans and I totally trust the vet that I worked with. Other puppy owners I worked with (so living in the same area) may have gotten their puppy vaccinated every 3 weeks, or every 4. Almost without exception vets will recommend the final vaccination around the 16 week mark. But maybe your vet has other reasons - I recommend asking!
How it works for puppies is, most puppies have maternal antibodies, or natural protection against common diseases like distemper or parvovirus. However, this is not guaranteed, and it depends on if the mother has antibodies for those diseases to pass on, AND if the puppy drank the colostrum (first milk), AND how much colostrum the puppy got. So you can have puppies from the same litter who will lose maternal antibodies at different times depending on how/when they nursed from the mom. So just think, the mom's milk may or may not offer protection but only if the puppy drinks enough of the milk at a very certain time.
Maternal bodies block efficacy of vaccinations though. So theoretical situation... if a puppy still has maternal antibodies at 9 weeks of age and is vaccinated at 9 weeks of age, the vaccine will not be effective but the puppy is still protected from certain diseases. But when the puppy is, say, 10 weeks of age and the maternal antibodies drop off, and the puppy does not get another vaccination, the puppy is completely vulnerable and can contract the diseases.
This is why puppies are vaccinated multiple times. Like storyist said, it's not that each vaccine makes the puppy more protected. The idea is to offer multiple opportunities for the vaccine to take effect. And vets/owners are trying to catch that very small window when the maternal antibodies first drop and the puppy is first vulnerable. Regardless if it happens at 7 weeks, 10 weeks, 15 weeks... WHEN the vaccine is delivered after the puppy's maternal antibodies are gone, it is effective and the puppy does not need further 'boosters' technically, until the recommended regular schedule like every 1-3 years. However, I did a lot of digging into titering puppies (basically, "can I find out if my puppy's vaccine worked at X weeks of age so I don't need to do another one?") and the short answer is no. The safest, most effective thing to do is to vaccinate regularly. And the most recent research is suggesting that the absolute maximum cutoff for maternal antibodies is around the 5 month mark, not the 16 week mark as commonly believed.
Disclaimer - I'm not a vet or in the medical field. I just work very closely with a lot of puppies and vets and I need to know this stuff for my job.
Also, I live in an area where parvo and distemper are rare. But I can think of two unique cases in the last year... One where an older puppy did not finish it's vaccination schedule, contracted parvo, and died. And one where a 9 month old dog with unknown vaccination history contracted parvo, and was fine after 1 week of treatment.