The Counter counts up by increment for each pulse on one input, and down by decrement for each pulse on the other. Right clicking the Counter opens a GUI to allow the maximum count, increment, and decrement to be set. Each output is on when the pointer reaches the end of range in that direction.
The Counter could possibly be used to keep track of people who enter and exit an area. Have the counter go up each time someone goes in, and go down everytime someone exits. That way, if it's negative, someone broke in, and if it's positive, someone's still inside.