The advice you have been given is absolutely correct; it is recommended that puppies remain in a controlled environment and only exposed to known vaccinated dogs until after their final puppy vaccination. I totally understand that you want to show off your new family member and can’t wait to get them out walking with you but it’s only a short wait and well worth it!
Puppies acquire maternally derived antibodies from their mother’s colostrum early in life. These antibodies are great but they can interfere with the effectiveness of the vaccines administered by vets in the first few months of a dog’s life. This is why we need to give puppies booster vaccinations until the maternal antibodies are out of their system and the vaccine can work as it would in an adult dog.
Puppy school or play dates with vaccinated dogs are vital in allowing your impressionable puppy to learn playing and social skills. 1 week after the final vaccination (usually at or soon after the age of 16 weeks) your puppy will be protected from nasty viruses such as distemper and parvovirus which can be picked up from the environment. A booster is usually then required in 12 months time and for core vaccines, every 3 years thereafter.