The Nyquist–Shannon theorem is the mathematical rule that says how often you have to sample a signal to capture it without losing information. Spelled out: if a signal contains details up to a maximum "frequency" — how many up-and-down patterns per unit of time or space — you must sample it at least twice that fast to preserve all of them. Sample slower, and the details collapse into wrong patterns called aliasing that look like something else entirely.
In video this turns into two concrete rules. Spatially (resolution), to capture a fine texture of a certain detail level, the camera needs at least twice as many pixels horizontally and vertically as the texture has details — otherwise you get moire, jagged stair-stepping on near-horizontal lines, shimmering in the wind in a wheat field. Temporally (frame rate), to capture motion of a certain speed, the camera needs at least twice the frame rate that the motion oscillates at — otherwise you get the famous "wagon wheels spinning backwards" effect or stuttering rapid motion.
For a product team, the theorem isn't something you tune directly, but it sets the fundamental limits on what video can capture. It explains why 4K isn't just "twice as many pixels as 1080p" but allows fundamentally different content (you can read small text in a wide shot), why 60 fps captures sports cleanly when 30 fps shows judder, and why downscaling a 4K master to 1080p with a proper anti-aliasing filter looks better than the same scene captured natively at 1080p. The theorem is the reason "shoot at the highest quality your pipeline can handle, then downscale" is sound production advice — it lets you control the sampling correctly rather than discovering it failed at capture.
