Energy moves, the medium stays
Put a light plastic ball on the water and make a wave. The ball does not sail away with the wave — it bobs up and down where it is.
For the ball to move up and down at all, energy has to reach it. That energy was brought by the water wave.
The most important property of a wave: it carries energy from one place to another, without carrying the material of the medium along with it.
What the water itself does
As a wave crosses a water surface, the water particles at each place move up and down. They do not move along in the direction the wave is travelling.
Easy to mix up
A wave moving across a pond looks like water flowing towards the bank. It is not: the pattern moves, the water stays. Watch the ball, not the ripple.