Parallax

In the Settings menu from the main menu in Terraria, the Parallax option controls how much the background scrolls relative to the foreground.

A setting of 0 (default) will have the background (which consists of sky, walls, etc) scroll with the foreground (what you walk on and bump into etc). A setting of 100 will scroll the background tiles at a high speed compared to walking just a little to the left or right.

Settings of 0-100 (inclusive) are available in the current v1.0.2.

This effect is most noticeable underground when you can see the dirt backgrounds scrolling when you move and have parallax set high.