Sample rate is the resolution of time in digital audio: 44,100 measurements per second on CDs, 48,000 in most production and video work, higher in some studios. Each rate captures frequencies up to half itself, its Nyquist frequency.
The 44.1 kHz number is history frozen into a standard, chosen in the era of storing digital audio on video equipment, and it persists because it comfortably covers the roughly 20 kHz ceiling of human hearing.
For real-time systems the rate also ticks the clock: latency budgets, buffer sizes, and analysis windows are all measured in samples, so the rate converts every engineering decision into milliseconds.