Light Slows Down
Light is the fastest thing in the universe, but it's hard to move through water because water is denser than air. When light travels from air into water, it slows down instantly. This change in speed causes the light to 'veer' or bend, a process scientists call 'refraction'.
The Bicycle Metaphor
Imagine a bicycle riding from a smooth sidewalk into a patch of thick sand at an angle. The first wheel to hit the sand slows down first, causing the whole bike to pull or turn in that direction. Light does the exact same thing when it hits the surface of the water.
A Brain Trick
Your brain thinks light always moves in perfectly straight lines. When the 'bent' light from the straw reaches your eyes, your brain 'draws' the straw where the light would have been if it hadn't slowed down. This creates the illusion that the straw has snapped or moved to the side.