The word binaural means “with two ears”. To experience the Binaural Beats, you will need headphones that can present you different sounds from different channels. (Most headphones have this feature, so you do not need special gadgets to experience this illusion!)
When hearing the Binaural Beats, the two ears receive slightly different auditory information (sounds), and this results in the perceptual experience of a different, third, sound. In the example we have here, two audio channels play sounds with slightly different hertz. The hertz is a unit of time which measures frequency. Frequency is a measurement of how often something happens. A frequency of 1 hertz means that something happens once a second. In this example, the left audio channel continuously plays at 100 hertz, with the right channel gradually moving up one hertz in frequency at a time (101, 102, 103 etc). The difference between the sound coming from the left channel and the sound coming from the right channel creates an experience of a third type of sound, which has a beat, or a rhythm. But there is no actual beat or rhythm. You can observe this by removing one of the headphones and putting it back on again. The difference between the two frequencies dictates the frequency of the beating per second, so a difference of two hertz leads to two beats per second, and as the frequency difference becomes greater it becomes more difficult to distinguish the individual beats.
Typically, discussions of illusory and hallucinatory experiences focus on visual experiences. But auditory illusions and hallucinations (and illusions and hallucinations in other sensory modalities, 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, such as audition, touch, taste, smell, and so on.
There is an interesting question whether the experience of the third sound in the Binaural Beats should really count as an illusion or a hallucination. Illusions are usually taken to consist in the misperception of some property of an object. For example, a clear example of an auditory illusion is the Doppler effect in which one experiences a property of the note—its pitch—as being lower than it really is if the source of the sounds is moving away from one. However, when listening to Binaural Beats one has an experience as of an extra note that does exist. This seems to most closely conform to the definition of a hallucination—an experience as of some object that does not amount to the perception of a worldly object. A full discussion of illusion and hallucaintion can be found in Macpherson (2013), and a diffierent account of illusion and hallucination can be found in Macpherson and Batty (2016).