It is a tool that measures how fast someone is driving. It is a rectangular metal block with a handle. It has a screen on the back which tells how many miles per hour a vehicle is going by using green digital numbers.
Role in episode
SpongeBob tattles on Patrick for going slightly over the speed limit, but since Patrick stops immediately, the police merely warn SpongeBob not to tattle, instead of doing anything to Patrick. The meter gun is a key item in the Bikini Bottom Police Department, and is used to check the speed of boatmobiles.
It uses Imperial units (mph) which implies that Bikini Bottom uses the Imperial System.