If one speaks of the fact that one gets blackbody radiation in good approximation by a cavity with hole, does one mean as blackbody this hole, i.e. the place where the radiation exits from the cavity? Then the concept would make much more sense for me, however I find the idea difficult that the blackbody is then only a thought object and no material object, because we are only talking about the hole.
Black body was originally defined to be a thought object, but in a slightly different sense: it is an hypothetical object which absorbs all EM radiation falling on its surface, and reflects (from its surface or inside) none of the incoming EM radiation (it also transmits no incoming radiation to the other side). It can however emit EM radiation of its own, in the sense that characteristics of the emitted radiation such as frequency spectrum or angular distribution of emission intensity depend only state of the radiating body (its absolute temperature), not on other sources which may have supplied the radiation energy in the past.
Then the question of how to approximate this hypothetical body for the purpose of measuring black body radiation arose. There are several possibilities, and there was an important series of experiments by Lummer and Kurlbaum, and by Lummer and Pringsheim. They made a specially shaped cavity with metallic walls reflective to EM radiation, with large inside surface, covered with well-absorbing layer (metal oxides) and with a small hole in the reflective wall to study properties of the emitted radiation.
Such a cavity is not itself a black body in the original sense, because it reflects substantial part of incoming EM radiation on its outside due to its metallic reflective walls; but the hole in the cavity behaves as black body surface of the same size as the hole, because any radiation energy that comes in through the hole will lose any characteristics and those cannot be detected in outgoing radiation from the hole.
This is because the radiation that comes in through the hole interacts with the absorbing layers in such a way that its energy gets dissipated into many different frequencies and directions. A radiation beam reflects many times and dillutes itself in frequency and direction; the hole is emitting radiation that reveals only the cavity inside's temperature, nothing else. This makes the cavity insides behave as perfectly absorbing body, a black body.
When the electromagnetic theory of light of Maxwell became well validated by most data at that time, people started thinking of various solutions of the equations, with different boundary conditions. One of them was Electromagnetic waves in a cavity. At the time the hole was not considered, but what was calculated was the spectrum of frequencies that could be trapped in a cavity. In an experiment, a hole would radiate out those frequencies to check the formulae.
This led to the classical formula versus the quantum formula to check with the data. The classical led to the ultraviolet catastrophy (seen in this image, see the links for the formulae)
The quantum solution avoids the catastrophy, has been checked against data, and the black body formula fits the radiation coming out of a body, usually approximately, due to extra corrections from the complexity of the matter constructing the black body.
The hole concept for a cavity is just a differential sample of the radiation impinging on the walls of the cavity and getting out, and as the reverse process is mathematically possible, the hole is how radiation can enter a cavity.
does one mean as blackbody this hole, i.e. the place where the radiation exits from the cavity?
Yes. The point is that the hole "absorbs" all radiation impinging on it, because it is a hole, so the radiation just goes on through.
In practice, we do not usually consider "holes," but rather physical objects that absorb most of the radiation that hits them.
Objects that are literally black in color (e.g., a black tee-shirt) absorb more radiation than colored objects (e.g., a pink tee-shirt). This is what make them black (they don't reflect any/much visible light), and this is why we use the term "black" body.