History: What does the Nyquist-Shannon theorem mean to digital audio sampling rates?

What does the Nyquist-Shannon theorem mean to digital audio sampling rates?

• The sampling rate needs to be half the highest audible frequency.
  Other direction.
• One needs to change the array of integers back into an analog signal.
  This is the job of the computer's sound card.
• The sampling rate needs to be twice the highest audible frequency.
  Excellent!
• One needs to change the analog signal into an array of integers.
  This is the function of a converter.