SNAP stands for the Supplemental Nutrition Assistance Program. It used to be known as "food stamps". In some places, it is also known as another name, such as "Link" in Illinois or "Calfresh" in California. It is sometimes referred to as "EBT", which refers to the way money is made available, an Electronic Benefits Transfer, which is money put on a card, similar to a debit card.
SNAP provides money to buy food. It's issued on a monthly basis to people with low-incomes to supplement their grocery budget so they can afford food.
It is a federally funded program within the Food and Nutrition Services department of the USDA (United States Department of Agriculture). It is administered by the states, so each state has it's own unique application process.