Not all tap water is the same, even if it looks the same. And although water varies widely, hard isn't necessarily better than soft or vice versa.
Hard Water Defined
The definition of "hard" water is water with a significant amount of minerals in it, often calcium and magnesium. These minerals are not harmful, and sometimes improve the taste of the water. Water isn't hard in its purest form, but can pick up these minerals and become hard as it passes through wells or materials with minerals in them.
Soft Water Defined
Soft water is, as you can imagine, the opposite of mineral-rich. Soft water contains little or no trace minerals or other elements, and can occur naturally or through water softeners that remove elements. Soft water sometimes has an unpleasant taste and isn't preferred for drinking.
What's the Difference?
Neither type of water is dangerous for you or your home. However, many homeowners prefer to soften water if they have particularly hard water in their home to extend the life of their appliances and reduce the need for cleaning. This is because hard water can leave behind scale (deposits of minerals) wherever it goes, turning stainless steel white and building up inside pipes. It's inconvenient and causes extra maintenance requirements, but it's not a hazard to health.
When you have overly soft water, however, you can end up with stains and chlorine resistance. Soft water is preferred for cleaning since it keeps glasses shinier, clothes softer, and showers freer of build-up.