Short answers, pulled from the story.
A computing palette is the set of colors available for rendering an image, often implemented as a color lookup table (CLUT) where each color is assigned an index number. Pixels reference their color by index rather than storing full color data, reducing storage from 24 bits per pixel down to as few as 8 bits per pixel. The GIF file format is a well-known example, using 256 colors each assigned an 8-bit index.
An adaptive palette is chosen directly from a single image by selecting its most frequent colors, giving better fidelity to that image but requiring the palette to be reloaded for each new image. A master palette is a fixed universal set designed to represent the full RGB color space in miniature, allowing multiple images to be displayed simultaneously without reloading palette data.
The 6R by 6G by 6B arrangement produces 216 colors and matches the Web colors standard, leaving 40 reserved slots in a 256-entry palette for special-purpose color indices. Alternatives include 6R by 8G by 5B for 240 colors and 6R by 7G by 6B for 252 colors. Blue receives fewer levels because the human eye is least sensitive to blue compared to red and green.
One palette entry is designated as the transparent color, typically index 0. Pixels carrying that index reveal the background layer rather than displaying a color, enabling image overlay for sprites, pointers, and video titles. GIF natively supports this designation; PNG extends it further by supporting alpha channel values per palette entry for semi-transparency.
The Commodore 64, MSX, and Amiga all supported sprites and full-screen video overlay at the hardware level. In these systems the transparent palette entry number was fixed by the hardware, conventionally set to entry 0.
Windows maintains a single shared system palette in RAM that mirrors the display hardware's physical color registers. Each application defines its own logical palette of up to 256 colors, which the system realizes by matching logical colors to system palette entries or evicting least-used colors to make room. The foreground window receives priority, and background windows may appear corrupted when palette slots run out.