The reason why a clock stops when you look at it is a result of an illusion called chronostasis.
It's not that the clock actually stops when you look at it, but instead it's your brain briefly editing out the blurriness that occurs during rapid eye movements.
When you shift your gaze to the clock, your brain then fills in the gap with the image of the second hand of the clock in it's current position, which makes it seem like it has paused for a moment.
When you move your eyes from one point to another point, such as from a wall to a clock, your eyes make rapid and jerky movements that are called saccades.
And during these saccades that your eyes are making, your vision is actually blurry.
Your brain then suppresses the visual information during this movement to avoid seeing a blur.
Instead of showing you a blurry image, your brain fills in the gap with what is perceives to be the most likely visual information at the moment your eyes settle on the new focal point.
And when you look at a clock, your brain back fills this gap with the image of the second hand in it's current position.
This can make it seem like the second hand froze for a moment before continuing it's movement.
The illusion is more noticeable with clocks which have a visible second hand, especially those with a ticking sound, because we expect the second hand to move in a consistent and predictable manner.