people use a variety of methods to wash clothes. usually after adding the soap , they beat the clothes on stone ,or beat them with a paddle, scrub with a brush or the mixture is agitated in a washing machine. why is agitation is necessary to get clean clothes? short answer

Agitation is needed to clean clothes because soap breaks down the dirt, but the dirt still sticks to the cloth. When the clothes are rubbed, beaten, or moved around, friction is created. This friction loosens the dirt from the cloth, allowing the water to wash it away and make the clothes clean. 
For example If a shirt has mud on it, simply soaking it in soapy water may not clean it completely. Scrubbing it with a brush or washing it in a machine helps loosen the mud, making the shirt clean.