Source: Woodrow Wilson Foundation. Water molecules want to cling to each other. This inward net force causes the molecules on the surface to contract and to resist being stretched or broken.
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However for a molecule on the surface of the liquid, there will be a net inward force since there will be no attractive force acting from above. Thus the surface is under tension, which is probably where the name "surface tension" came from.
At the surface, though, the outmost layer of molecules, has fewer molecules to cling to, therefore compensates by establishing stronger bonds with its neighbors, this leading to the formation of the surface tension. Why bubbles are round: The surface tension of water provides the necessary wall tension for the formation of bubbles with water.
Those on the surface have no neighboring molecules above and, thus, exhibit stronger attractive forces upon their nearest neighbors on and below the surface. However, in practice it is fine or even preferred to have a low level of dampening water absorption because of a phenomenon that occurs when water settles at the surface of paper.