Not really? I don't want to say your teacher is wrong, but that description does not conform with my understanding of surface tension.
Think about water as an example. In liquid water, you have a network of hydrogen bonds that are very stabilizing and favorable. A water molecule in the middle of a drop is surrounded by other water molecules, and is fully involved in these stabilizing interactions. However, at the surface, things change. The part of the water molecule at the interface with air is no longer stabilized by these favorable interactions, and so it wants to retract back into the liquid, where it can engage in more hydrogen bonding. Expand that to all molecules on the surface; they all are trying to contract inward, and so the liquid takes on a spherical shape to minimize the number of molecules that are in contact with the surface (spheres have smallest surface area: volume ratio). The more a liquid prefers self-interactions to interactions with a surrounding substance (air, oil, etc), the higher the surface tension. So look at water and diethyl ether. The former has a much higher surface tension with air. Why? Because the ether solution lacks the capacity to form strong hydrogen bonds, the molecules at the surface have less 'incentive' (so to speak) to get back into the middle of the solution.