Surface tension in liquids is caused by attractive forces between the molecules of the liquid. These forces are called cohesive forces.
Water,for example, has polar molecules. This means that each molecule has a slightly negative charge at one end and a slightly positive charge at the other. The negatively charged end of one molecule is attracted to the positively charged end of another molecule, and the two ends "stick" together.

When you put liquid in a beaker, you probably notice that the sides of the liquid sit up kind of high on the sides of the beaker, forming what is called a meniscus. This happens because of an attraction between the glass and the liquid molecules. This attraction is called an adhesive force because it occurs between two unlike molecules. The adhesive force between the glass and the liquid is greater than the cohesive force between the liquid molecules; therefore, the liquid is pulled up the sides of the beaker toward the glass.
I hope this helps!