Countdown mechanic is about finishing a task in a limited amount of time. Normally it is a really short time limit, for example a time trial from Crash Bandicoot games or any racing game. This is supposedly there to keep a level of excitement when being under a time trial.
This image is taken from the Crash Bandicoot: Wrath of Cortex. As you can see at the bottom of the image there is a timer which shows how much time you got left for the task you’re doing, or how much time you’ve already spent doing a specific task.
This image is showing a racing game which has a time trial and a countdown on the top right corner. It says ‘Gold’ this probably means that in order to get a gold reward for this race you have to complete it in under the specified time.
The way I would implement this mechanic into my game, would be to include a time trial as an optional thing which could allow the player to ‘speed run’ the game.