In indexed images/modes, palette swap is a palette effect where the appearance of an image is changed by swapping one or more colors in the palette with other colors.
In the strict sense, palette swap refers to exactly that, changing palette entries to re-color an indexed image.
In a wider sense, regardless of technical hardware details or how the re-coloring of the art is actually being done, any change of the color scheme of a piece of art may also be called a palette swap.
A palette swap can be simple, as in the example here, where the swap simply re-colors parts of the image or it can be more advanced to store multiple images in a single indexed image (see also steganography) as demonstrated in the video linked below.
further reading/viewing: