I think its defined as a highly populated area of poor people where a grocery store isn't really close by, or even a low populated area of poor people where a grocery store is really far away.
Or as the gubment' says:
To qualify, an area must be a low-income census tract where a substantial number or share of residents has low access to a supermarket or large grocery store:
To qualify as a “low-income community,” a census tract must have either: 1) a poverty rate of 20 percent or higher, OR 2) a median family income at or below 80 percent of the area's median family income;
To qualify, an area must be a low-income census tract where a substantial number or share of residents has low access to a supermarket or large grocery store:
To qualify as a “low-income community,” a census tract must have either: 1) a poverty rate of 20 percent or higher, OR 2) a median family income at or below 80 percent of the area's median family income;
To qualify as a “low-access community,” at least 500 people and/or at least 33 percent of the census tract's population must reside more than one mile from a supermarket or large grocery store (for rural census tracts, the distance is more than 10 miles).
Credit: Bud Kennedy. Complete map here.