Most of our water softeners add salt to the water in a process called ion exchange. This actually changes the chemistry of the water, changing the harsh minerals in the water, usually calcium, from affecting the way that soap acts to get things clean. Softened water is easier on the skin, but hard on plants because of the salt. Most people will install a cold water by-pass to provide untreated cooking water, drinking water and even the outdoors hose bib. That simply requires tapping off some water before the connection to the water softener.
Others use an alternative scheme and only soften the water heading to the hot water tank, leaving all the cold water in the house untreated. If you always clean with at least some hot water, that works fine, uses less salt and does not affect the plants.