Groceries used to give them out based on your purchase amount, and you saved them up to buy things from a catalog. You put the kids to work licking the things and pasting them into booklets.
We mainly saved Top Value stamps in my family. I suppose that's what the dominant grocery in the area gave out, and there was a redemption center, a store really, nearby. The last time I remember going there with my mother was in 1975, to pick up an end-table with built in lamp.
from the Wikipedia article on "Green Stamps"
S&H Green Stamps (also called Green Shield Stamps) were trading stamps popular in the United States from the 1930s until the late 1980s. They were distributed as part of a rewards program operated by the Sperry and Hutchinson company (S&H), founded in 1896 by Thomas Sperry and Shelly Hutchinson. During the 1960s, the rewards catalog printed by the company was the largest publication in the United States and the company issued three times as many stamps as the U.S. Postal Service. Customers would receive stamps at the checkout counter of supermarkets, department stores, and gasoline stations among other retailers, which could be redeemed for products in the catalog.
S&H Green Stamps had several competitors, including Triple S Stamps (offered by Grand Union Supermarkets), Gold Bond Stamps, Blue Chip Stamps, and Plaid Stamps (a project of A&P Supermarkets).