A lather is the froth soaps and detergents produce. Lathering also means to soap yourself up, and a lather can be a state of extreme agitation.
When you're taking a shower, you make the soap frothy: this is a lather, and you're lathering when you create it. Rubbing soap on your body is also called lathering. Since lather is a stirred-up form of soap, it can also apply to emotions that have been stirred up. Someone upset is in a lather. Getting in a lather usually results from worry or anger, and it's an unpleasant state of mind.