Colorwalks are a way to create theoretically continuous sequences of colors (actually often discrete in practice) that transition smoothly and aesthetically. They can be used to create high-quality, aesthetic pleasing gradients, color transitions/animations, or palettes.
A color walk is defined by a color volume (such as an rgb cube, hsv cylinder, L*a*b volume, etc) and a path through that volume/space. The path, ideally a continuous function such as a spline or arc, is sampled to create the sequences of colors. Using a color space that has a near-isomorphic mapping of perceptual distance to euclidian distance, such as L*a*b, will result in a smoother colorwalk (I think).