Translation: This isn’t exactly jargon, because food aid is exactly what it sounds like. Food, given away to people who need it. It may be given in a food-for-work scheme, where the donor has people do work for the common good such as digging latrines or rebuilding schools in return for the food. It may just be distributed according to some criteria about who is sufficiently in need (very often female-headed households).
The thing about food aid, though, is it is almost never locally purchased. It is generally produced in the donor country, and purchased from those domestic farmers, then shipped abroad as food aid. This supports a domestic market and farmers in the donor country. If food is purchased in the recipient country from local markets, we usually don’t call it food aid. We just call it hunger relief, or “an effort to improve food security.”