It is not very common for us to cross our fingers and then touch objects between them. The effect that you get of feeling two objects is due to the fact that our brain is not used to receiving tactile information under those circumstances. When the spherical object that is in the middle of your two (crossed) fingers touches your fingers, it touches on the “outsides” of both of your fingers. Suppose you are trying this with your right hand. What happens is that left side of your index finger is touching the object, and the right side of your middle finger is touching the object. When this sort of thing happens in normal circumstances—i.e., when your fingers are not crossed—you are typically in contact with two objects: one touching your index finger from the left, and one touching your middle finger from the left. So when your fingers are crossed, your brain “assumes” that this is what is happening again, hence creating the inaccurate experience of a second object touching your fingers.
This is called Aristotle’s Illusion because it was first recorded by the ancient Greek philosopher Aristotle (see Aristotle & Ross 2001). Although it is called an illusion, one might think that it is actually a case of hallucination. In cases of illuson, one perceives an external object, but misperceives some of its properties. In cases of hallucination, one has the perceptual experience of an object which doesn’t exist. Here, it might be argued that we are experiencing a second object which does not exist in reality, hence suggesting that this is a case of hallucinatory experience.
However, there is some reason to resist this explanation and to think of the case as one of illusion, for what is going on bears an interesting similarity to cases of double vision, in which one has a visual experience as of two objects when only one is present. (For example hold your index finger up very close and in between your eyes and you will experience two index fingers, whe in fact there is just one present.) Philosopher E. J. Lowe (2000, p.109) claims that this phenomenon is best thought of as perceiving the finger twice—once with each eye— that results in two experiences of a finger. At least one of the experiences of the finger, but likely both, will then be illusory with respect to the location of the finger. Transferring this line of thought to Aristotle's illusion, one would say that one feels the object twice—once with each finger—and this results in two experiences of the object, at least one of which is ilusory with respect to location.
Philosophers disagree as to how we should best explain illusions and hallucinations, and some theories of perception may accommodate one phenomenon better than they do the other. See Macpherson (2013) for a detailed overview of various philosophical approaches to hallucinatory perceptual experiences, and Macpherson and Batty (2016) for a reconsideration of the difference between illusions and hallucinations.
Typically, philosophical discussions of illusory and hallucinatory experiences focus on visual ones. But tactile illusions and hallucinations (and ones in other sensory modalities such as audition, taste, smell, and so on, including cross-modal ones) are also interesting. Illusions and hallucinations in general provide us with cases in which what we experience doesn't seem to match reality. If that's right, we are not experiencing reality, and we can ask what it is that we are experiencing. If that's not right, then we can ask why we appear to experience something that doesn't match reality, and whether we really are experiencing what we take ourselves to be experiencing. Illusions and hallucinations in sensory modalities other than vision show us that this issue affects experiences in other modalities.