This is a tricky question, because it depends on what kind of wave you're talking about. Here's the breakdown:

The Wave Itself:

* The wave itself moves *forward*! This is the direction the energy travels. Think of dropping a pebble in a pond – ripples move outward from the point of impact.

The Medium:

* The medium (the stuff the wave travels through) moves *up and down* (or side to side). In the pond example, the water molecules themselves move up and down as the wave passes.

Putting it Together:

* The wave carries energy *forward*, but the medium carrying the wave moves *up and down*. This is why it's important to distinguish between the motion of the wave itself and the motion of the medium.

Examples:

* Ocean Waves: The wave moves toward the shore, but the water molecules themselves primarily move up and down (with a slight back-and-forth motion too).

* Sound Waves: Sound waves travel through the air, causing air molecules to vibrate back and forth. The sound wave moves forward, but the air itself just vibrates.

Let me know if you have any more questions!