The candystick, or candycane, is a sweet shaped like a small walking stick, striped like a barber's pole. We buy them from sweet shops.
It gets into ( usually ) Christmas services because of a story, which is probably apocryphal - see, for example, here or here. We were careful always to call it a story. Fact or fiction, it makes a point very well.
Here's a picture; click it for a separate ( JPG ) version.
We have used candysticks in some of our services :