What does "16-bit" mean when referring to digital audio?

Converting sound into a digital format requires taking samples of the original sound wave at regular points in time. These samples numerically represent the relative strength, or amplitude, of the analog wave as it varies over time. For digital audio, these numbers are recorded in binary notation. When digital audio is advertised as 16-bit, we mean that the numerical samples of the artist's recording were recorded as 16 digit-long binary numbers.