The Day stick is a long one- or two-handed cudgel (blunt weapon like a baseball bat or a club). It is used by Judges for riot control and less-than-lethal attacks on aggressive perps. It has a titanium core, as demonstrated when one perp attempted to slice though it with a chainsaw to no avail.
It gets its name because you can use it to "Beat the day lights" out of the targeted perp. These weapons are also called night sticks which means basically the same thing. Also, these weapons are called police batons in this Judge Dredd universe they are known Officially as Judge Batons. Historically when Police Forces were first organized in the 19th century they were originally called "Billy Clubs".