The Necker Cube Ambiguous Figure is named after its creator, Louis Albert Necker (1786-1861), who first published the illusion in the London and Edinburgh Philosophical Magazine and Journal of Science in 1882.
The Necker Cube Ambiguous Figure belongs in a large class of illusions where a two-dimensional figure, or three-dimensional object can be seen in two or more sharply distinct ways. There are many example of ambiguous figures which you can search for in this illusions index.
One reason that the Necker Cube is so interesting is that although it is perhaps most natural to see the image as one of two cubes differently oriented in space, it is possible to see it as simply a 2-D figure on the page. Therefore the Necker Cube is three-way ambiguous. The fact that one can see the image as both 2-D and 3-D feeds into the debate about whether visual experience represents 2-D or 3-D space. If the 2-D/3-D Gestalt switch is a change in the visual experience itself as seems to be the case (rather than a change in our beliefs about the image) then this would best be explained by visual experience being as of 3-D space.
Relatedly, there is another version of the Necker Cube which looks like a 2-D figure at first, but can be seen as a 3-D cube also, as illustrated below.
There is some controversy over how the Necker Cube Ambiguous Figure works. It is generally agreed that the retinal image is constant when experiencing the illusion, but what is not agreed is whether the visual experience of the cube changes when the perspectival switch takes place, or whether the experience itself does not change, and it is some post-experiential belief, judgment, or other mental process which changes. The Necker Cube, among other ambiguous figures, has been cited in debates over this issue (Silins 2015: §2.4).
This issue is intertwined with more general questions about the modularity of mind and cognitive penetration. To explain: on the hypothesis that the mind is modular, a mental module is a kind of semi-independent department of the mind which deals with particular types of inputs, and gives particular types of outputs, and whose inner workings are not accessible to the conscious awareness of the person – all one can get access to are the relevant outputs. So, in the case of visual illusions, for example, a standard way of explaining why the illusion persists even though one knows that one is experiencing an illusion is that the module, or modules, which constitute the visual system are ‘cognitively impenetrable’ to some degree – i.e. their inner workings and outputs cannot be influenced by conscious awareness. It is still an open question regarding the extent to which perceptual modules are cognitively impenetrable, and ambiguous figures are employed in debates to try and answer that question. One way in which ambiguous figures might support the claim that visual processing is impenetrable to a significant degree is that the Gestalt switch is hard to control – often one will see a figure one way or another even if one is trying to see it the other way. Macpherson discusses this phenomenon and its implications in her 2012 paper. Further, there is some evidence from neuroscience that, for at least some ambiguous figures, there are significant changes in early-stage visual processing in the brain when the Gestalt switch is taking place, which might support the hypothesis that Gestalt switches in general are changes in the experience itself rather than in downstream mental processes like beliefs about that experience (see Kornmeier & Bach 2006, 2012).
Finally, ambiguous figures have been cited in debates about whether the nature of experience can be fully accounted for by appealing only to its representational content. Some philosophers and cognitive scientists distinguish between the phenomenal character of an experience – i.e. what it is like for a conscious subject to undergo that experience – and its representational content – i.e. what the experience is about. Some philosophers, known as ‘representationalists’ argue that the phenomenal character of experience can be accounted for fully in terms of the representational content of experience. One motivation for this argument is that representational content seems easier to ‘naturalise’ – i.e. for its nature to be explained in purely materialist terms by appealing solely to physical entities like brain states. Phenomenal character, on the other hand, seems much more resistant to attempts to naturalise it. But if phenomenal character can be fully accounted for in representationalist terms, then this would make the naturalising of phenomenal character seem much more tractable. And, ambiguous figures are among the key examples discussed in debates about whether phenomenal character can be fully accounted for in representationalist terms. For example, Macpherson (2006) has argued that the changes in phenomenal character that occur when experiencing some ambiguous figures cannot be explained in naturalistic, representationalist terms. Macpherson’s 2006 paper provides an overview of the general debate and its many moving parts.