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This video by Gary the Water Guy explains How a water softener works.

Many people have water softeners or are considering a water softener but are not sure how they work.  The following is the basic process a water softener goes through to soften your water.
Water softeners have two tanks, one that is smaller diameter and is sealed with a control valve at the top, which is called the media tank. The other tank (that looks like a garbage can) has a lid that you open that holds the salt, which is called the brine tank.  Sometimes the smaller tank is actually inside the larger tank. 
All of the water in the house runs through a bed of small plastic beads that look like Honey Comb cereal but are a lot smaller.  These beads fill most of the media tank.  As the water is passing over these beads the hardness (the calcium and magnesium) sticks to the beads and is removed from your water.
Eventually, the beads are covered with calcium and magnesium and needs to be regenerated so they can continue to soften the water.  The water softener automatically triggers the regeneration process, which typically happens at night.
The water softener starts the regeneration process by automatically backwashing all of the media and then sucking the salty water from the brine tank.  As the salty water or brine runs over the resin beads it releases the hardness from the beads.  During this regeneration process the calcium and magnesium, dirt and sediment are flushed from the beads and into the drain. 
The final step in the regeneration process consists of the water softener putting the correct amount of water into the brine tank to make brine so it is ready when the next regeneration is needed.

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