In Indexed Images/Modes where each pixel in the image refers to a specific color in a sequence of colors(=palette) (instead of holding the full definition of the color in each individual pixel itself), a number of visual effects such as Color Cycling and Color Fading can be achieved by manipulating the palette instead of manipulating the pixels themselves.
This was used a lot on old hardware as manipulating the definition of colors in the palette took much fewer CPU cycles than going through the image and changing the actual pixels themselves.
A simple example for a Palette Effect is just re-defining a color in the palette: If a thousand pixels in an image referred to color at index five in the palette and index five would hold Green and index twelve would hold Red, all thousand pixels could be changed to Red by changing the color at index five from Green to Red instead of going through the image and looking for every Green pixel and changing the pixel itself to refer to index twelve.
see also: Palette Structure, Palette Swap, Palette Swap - Color Cycling