How do they make realistic flowing water in video games?

My daughter showed me this video, which uses a location in Super Mario Galaxy 2 to show how game designers use scrolling layers and textures to create the illusion of flowing water. The video was created by a guy named Michael 'Jasper' Ashworth, who has a very cool website of elements, art, and levels from a bunch of Nintendo games that you can experiment with.

It's videos like these that make me love YouTube.