Soap decreases surface tension by changing the way water behaves on the surface. Hard and soft water react differently when soap is added to them.
Surface tension deals with the cohesiveness of molecules in a liquid. Cohesion refers to the attractive force between molecules of the same type. Water molecules cohere more strongly to one another than to air molecules, forming a surface layer that resists light pressure. Soap is a surfactant, meaning that if affects water at the surface. The molecules of a surfactant have hydrophilic (water-loving) ends and hydrophobic (water-repelling) ends. Introducing a surfactant to water causes the surfactant to line up so that the hydrophillic ends align with the water and the hydrophobic pieces align with the air above. This creates a new surface film of soap and interrupts the cohesive forces between water molecules.
The surfactant properties of soap are responsible for its ability to clean clothes. Soap disrupts the cohesion of water molecules, allowing the water to soak into clothes in a laundry machine. Hard water, however, is somewhat resistant to the action of soap. The additional molecules that make the water hard tend to clump together with soap molecules and drag them out of the solution, leaving surface tension more intact.