Responsive design makes a single layout work across different screen sizes and shapes. On the web that means phone to desktop; across a signage estate it means portrait and landscape, 16:9 and 32:9, a 10-inch shelf display and a video wall.
The reason it matters is that estates are never uniform. Sites open with whatever hardware was available, orientations differ by fixture, and a layout authored for one exact resolution has to be remade for every variant, which is how content stops being updated.
The caveat is that responsive is not the same as legible. A layout that technically reflows onto a small display can end up with text nobody can read from the distance that screen is viewed at. Viewing distance, not pixel count, sets the minimum type size, and a shelf display read from half a metre and a wall read from six need genuinely different designs, not the same one scaled.
The practical approach is a small number of deliberate variants (portrait, landscape, ultra-wide), each authored for its viewing distance, rather than one fluid layout expected to handle everything.