Surface tension is caused by the attraction between the molecules of the liquid. In the bulk of the liquid each molecule is pulled equally in all directions by neighbouring molecules, resulting in a net force of zero. At the surface of the liquid, the molecules are pulled inwards by other molecules deeper inside the liquid, but there are no liquid molecules on the outside to balance these forces, so the surface molecules are subject to a net inward force.
Remember, by Newton's second law, a net inward force produces an inward acceleration. Thus bulk water is unstable.
There may be a small outward attraction caused by air molecules, but air is much less dense than the liquid, so this force is negligible.
Dimensional analysis shows that the units of surface tension (Nm-1) are equivalent to joules per square metre (Jm-2). This means that surface tension can also be considered as surface energy. If a surface with surface tension γ is expanded by a unit area, then the increase in the surface's stored energy is also equal to γ. It follows then that the surface energy of a material is equal to one half of its energy of cohesion.