A Public Charge, as defined by the USCIS, is a person who is likely to become:
“primarily dependent on the government for subsistence, as demonstrated by either the receipt of public cash assistance for income maintenance or institutionalization for long-term care at government expense.”
In other words, a public charge is a person who cannot support themselves financially and depends on certain welfare benefits. People who are likely to become a public charge are not admissible to the U.S. and are not eligible to receive a permanent resident card. However, it's up to the government to try to predict if an applicant is a potential future public charge. So they are not looking at whether or not the sponsor is currently receiving such benefits, but whether or not the alien is likely to in the future.
Benefits that provide cash include Supplemental Security Income (SSI) and Temporary Assistance for Needy Families (TANF). Benefits that do not provide cash - such as the Supplemental Nutrition Assistance Program (SNAP) aka Food Stamps or subsidized housing do not factor into considering a person a public charge.