A sticker is a label having one single color. One sticker is attached to each face of every cubie (or whatever the shape is for the pieces) of a twistable puzzle, normally in different colors for each side (face) of the puzzle. Sometimes tiles are used instead of stickers.
For example, taking a 3x3 Rubik's Cube: the center pieces each have one sticker, edges have two, and corners have three. A cubic puzzle will normally have six different sticker colors. 12-sided puzzles like the Megaminx usually have twelve different sticker colors.
'Sticker' is often used as a term when talking about positions of faces of cubies, aspecially in BLD. The position of the 'sticker' is where the piece is, or where it shall go.