These 2D games display the foreground, including main game characters, as silhouettes, with a lighter background behind them to keep the foreground details visible. Many games use this art-style for the entire game while others only use it for a particular level or scene (such as the very opening title screen of Braid that forms part of the overworld).
Some suggest that a reason for the prevalence of this style relates to the ease of which these graphical assets can be developed. This could explain why it is a common style used in many smaller indie titles. Naturally, the 2D silhouette aesthetic applies its own constraints and these outlines of objects need to be carefully designed so that they immediately convey what an object is to a player just from its shape. Also, the main protagonist can get hidden by passing by similarly silhouetted foreground objects, so it must be ensured that this doesn't become a problem for identifying where the main protagonist is on screen.
2D silhouettes also naturally help create a particular atmosphere in the games where they are used, often one of mystery because many of the details of the world and character are kept hidden from view (e.g. Limbo, Lost in Shadow, Insanely Twisted Shadow Planet).