Color block prints have always been popular to produce inexpensive art. Although many cultures use relief printing, it was brought to it's highest level by the Japanese artists of the Seventeenth to the Nineteenth Centuries.
These prints were made using two lineoleum blocks - one for the lines and one for the flat colors. That there are more than two colors simply means you can ink different parts of the block with different colors.
These prints were made using water soluble ink, as was common with Japanese prints. Water soluble inks have the advantage of being easy to clean up and thin down (if needed). They also dry considerably faster than oil based inks. This can be advantageous - to print the second color the first should should be dry - and disadvantageous - the ink dries faster when spread out on the plate and brayer - that is, the ink roller. And of course oil based inks dry are waterproof when dry but water can ruin a print made from water soluble inks.