A computer user interface control that appears to be a standard button, but is actually does unexpected things when clicked. From "button that cons", not the contraction of "button control". The con comes from altering the expected behaviour of a button - from DOING something, to ASKING something.
A "line width" butcon in a paint program is a UI button that opens a drop-down selector for various line widths. Programmer should have used a specific drop-down UI control instead to provide visual hints to the user that clicking the UI control will open a drop-down.