When we move one end of a rope that has the other end attached to a wall, up and down , we can see the waves passing along the rope. The rope itself does not move forwards with the waves.
Although the wave energy moves from the vibrating source, the particles are not carried along with the waves. Hence, waves transfer energy without transferring particles.
There are different types of waves based on types of matter they aer able to travel through. Electromagnetic waves can travel through a vacuum. Radio waves, visible light and X-ray are examples of electromagnetic waves.
Mechanical wave is a type of wave that cannot travel through a vacuum. It needs a medium to travel. Some examples of mechanical waves are sound and water waves.
We can also categorize waves based on how the orientation of the particles relative to the direction of the energy propagation. They are transverse waves and longitudinal waves. A transverse wave is a wave in which the particles move in the direction perpendicular to the direction in which the waves moves. A transveres wave. An example of transverse waves is water waves.