There are two major screen technologies that are used in mobile devices today, LCD and AMOLED. On an LCD display you have a backlight that lights up the whole screen. To produce a black color the display will dim the pixels to prevent the backlight to slip through, and consequently producing a black color. This means that even if the whole screen should be painted pitch black the backlight will still be on behind the screen draining battery. A black background will therefore not affect battery drain if your phone is equipped with an LCD display (e.g. iPhone). On the other hand, AMOLED displays do not have a backlight like the LCD displays, instead each pixels emits its own light. This means that if the whole screen is to be painted black, the pixels won’t be emitting light. As a result, a black background will actually slightly reduce battery drain on phones with AMOLED displays (e.g. Samsung Galaxy S phones).