As Wikipedia says, a souvenir (from the French for "memory") is an object that is treasured for the memories associated with it. The term is used for items brought home from places visited. Such items are sometimes marked or engraved to indicate that their value is sentimental rather than practical.
To this we can add that souvenirs are usually bought by tourists and, therefore, are sold in the areas visited by tourists.
The most typical souvenirs from Budapest are handmade embroidered tablecloths, Halasi laces, national costumes and dolls dressed in such costumes, purses made of stiff leather, T-shirts with certain images and symbols, such as Hungarian flag or emblems. You will find these wares in Váci utca, Central Market, Castle Hill and Ferihegy Airport.
There are of course the famous Hungarian food and drinks - red paprika, goose liver, salami, Unicum liquor, pálinka (fruit spirit), wine from Tokaj and other famous types. But food and drinks can hardly be regarded as souvenirs. You are not going to treasure this salami for years, are you? Such Hungarian specialties are good as gifts for your family and friends, and you can buy them in some supermarkets (including those in Váci utca), Central Market and in Ferihegy Airport.
But if you are a collector of some kind or interested in buying antique, you may find what you are looking for in antique shops or specialty stores, such as Teddy Bear Shop or Kit Modell 1001.