Food at the market is self-supervised. It is up to the buyer, perhaps in conjuction with a Rabbi, to use the self-supe system to determine if the food meets their own Kashrus standards.
Halacha of Kashrus supervision
The Halacha, according to my understanding, is that one witness is sufficient in regard to establishing the status of something that can be forbidden or permitted. Food permissibility is one area where this principle applies. Kosher supervision requires only one witness to ascertain the Kashrus of the food.
The witness can be a man or a woman who is Halachically reliable and knowledgeable. Thus, a butcher who is reliable and knows the Laws of Kashrus does not require a separate Kosher supervisor in his store. The meat is Kosher if the butcher says it is.
Standard application of Kashrus supervision
The following is a discussion about food that may not be eaten according to the laws of Kashrus unless the food has been determined to be Kosher. That is, an apple that is right off a tree that you own is intrinsically Kosher, although one may need to check it for infestation. A piece of meat, however, requires verification that it is Kosher. This discussion is about products like meat, cheese, wine etc.
Many stores producing Kosher food have owners who are not Halachically reliable. That is, one is not allowed to trust the owner if he says the food is Kosher.
Say such a store wants to sell to people who keep Kosher. The store can hire a Kosher supervisory organization. The Kosher supervisory organization is called a Hashgacha.
The Hashgacha may station a reliable and knowledgeable witness in the store in order to establish that the food in the store is Kosher. This witness overseer is called a Mashgiach. Customers may then rely on the Mashgiach when he or she says the food in the store is Kosher.
An alternative to a Mashgiach always being present and in control when food is produced may be a Mashgiach who has the right to enter and leave the store at will — to inspect without notice.
A Mashgiach is redundant when the owner is a reliable witness; still, it has become the custom for many who observe the laws of Kashrus only to buy food which is under a Hashgacha.
Non-standard Kashrus supervision
The self-supervision Kashrus system (self-supe) takes a different approach to Kosher supervision.
First, a self-supe store is owned and run by a reliable and knowledgeable proprietor/manager. Next, much of the store’s operation is documented and placed online where it is accessible to the public. Finally, every customer is permitted to enter the store’s kitchen at any time that it is in operation.
The sum total of this approach is that the store’s kitchen becomes an extension of your kitchen. You browse the store’s website for information on the kitchen and kitchen production. You go in the kitchen. You watch the live feed as products are prepared.
Someone who keeps Kosher is aware of the provenance of the food and utensils in their own kitchen. They have access to their own kitchen. And thus they trust their food is Kosher.
With a self-supe store they have the same type of knowledge and access as if it was their own kitchen. If they like what they find on a store’s associated self-supe webpage, then they can be confident that the food they buy at the store is at least as Kosher as food from their home kitchen.
Peruse the premises of self-supe stores in person as well as virtually through the pictures, videos, and text on the store’s website. Pepper the store with your Kashrus questions. Self-supe stores welcome and encourage inquiries and investigations. Find out about the food and utensils; about how the food is prepared; and about the people preparing it. Know as much as if you had prepared the food yourself with your own handpicked kitchen staff and carefully monitored utensils.
Self-supe information includes details like when ovens were Kashered, which dishes and utensils were Toveled and when, who turned on the cooking fire, the basis for deciding each ingredient is Kosher, when the food was prepared, how vegetables were checked, info on taking Challah, Mechiras Chametz, and much more.
Vendors can answer general questions about a given ingrediens such as what it is, where did it come from, how was it made, who made/grew it, when was it made, why was it made, how did it get transported to here.