If we suppose that the phenomenon you describe is related with wave interference. A wave is a kind of mechanical disturbance in the medium through which it is travelling. A sound wave consists of areas of relatively high and low energy, in the form of relatively high and low pressure. To understand how sound is produced, consider a speaker. The cone or diaphragm of a speaker vibrates inwardly and outwardly in response to an electrical signal. These vibrations are typically very small, only visible with larger speakers. However, they all impart energy to the air in the same way. When the cone moves outward, it pushes the air forward that originally occupied that space. This air becomes locally compressed, forming a region of relatively high pressure. When the cone moves inward again, it recoils from the space that it occupied and leaves behind a partial vacuum, a region of relatively low pressure. The frequency and amplitude of the vibrations change the characteristics of the wave that is formed, and hence the sound that we perceive. When we hear the sound, our ears are being bombarded with air molecules of rapidly varying pressures. The signal is sent to the brain where it is interpreted.
As the sound wave progresses through the air, its energy slowly dissipates. This is why sound is louder closer to the source and quieter further from the source.
Wave interference occurs when two or more waves disturb the same air molecules. If a relatively high energy part of one wave combines with a relatively low energy part of another, the result is a region of air with an average of the two. In the most extreme case, the resulting pressure is indistinguishable from that of the undisturbed air, and is therefore undetectable by the ear. This situation is known as total destructive interference. In practice, however, interference is almost always partial. Similarly, if two high- or two low-energy parts of a wave combine, they can be summative. This opposite process is known as constructive interference.
To visualise this process, you may want to look at a video or two on-line. Note that water waves illustrate the concept extremely well, but the mechanisms by which they function are very different to the process described above.
Both constructive and destructive interference occur frequently wherever there are multiple sounds. However, their effects are generally minor in the natural world. Some of the commentaries above probably provide a more accurate explanation of the phenomenon you describe.