When you drop a stone in a pond, you displace the water on which the stone fell. Imagine the surface of water like a surface of rubber or elastic. The stone drops on this surface, and forms a depression in it. The surface exerts a force back on the stone causing the surface to try and regain its original shape.
Hence, the portion of the surface on which the stone fell starts going up and down (or oscillating). This causes the particles adjacent to the point on which the stone fell to also go up and down. Hence, in this manner, energy is transferred from particle to particle, and the particles on the whole surface start oscillating. Some of these particles go up and down in the same way (ie, when one is up, the other is also up; this is called being in phase) which results in the ripples you see.
The particles themselves do NOT move, they just go up and down in the same place. The force which causes the surface to regain its original shape is called surface tension.
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