why does soap and water remove dirt while washing?

Answer 1

Soap is a surfactant, that is is allows oil and water to mix. The reason some dirt will not come off your clothes if you just use water is that the dirt mixes with the skin oil and gets "glued" to the clothing. Any surfactant that you use will pull the oil off the clothes, taking some of the dirt with it and allowing the water to flush the rest of the dirt off the fabric.

Answer 2

Soap lowers the surface tension of water, making water wetter and more able to remove soil and dirt.