Why does surface tension act tangentially to the surface? Why is it not a vertical stress?
The properties of surface of a liquid are markedly different from the properties of bulk matter. A molecule well inside a body is surrounded by similar particles from all sides. But a molecule on the surface has particles of one type on one side and of different type on the other side. A molecule of water well inside the bulk experiences forces from water molecules from all sides but a molecule at the surface interacts with air molecules from above and water molecules from below. This asymmetric force distribution is responsible for surface tension.
Since we consider molecules to be very small spherical bodies, the surface force due to air and/or vapour molecules in contact with liquid water molecules will be tangential as the interaction between the two types of molecules takes place at their surfaces only. This gives the famous analogy of the surface to a piece of taut rope (just like a stretched rubber sheet).
The question that ponders one’s mind quite often is that how does the mass of a needle floating on the surface (which acts vertically) is balanced by tangential forces. From the mechanical point of view this can be explained easily. The tension is always tangential to the surface. The needle rests on the surface (which bends around it), and the surface exerts a tangential force, which in this case has a vertical component that balances the mass of the needle.