Hard water is caused by dissolved minerals in the water. This typically occurs in areas where there is a lot of calcium or magnesium in the bedrock that the water moves through on its way into your well. There are simple chemical test kits that can tell you if your water is hard, but most people know because hard water tends to cause stains in sinks, bathtubs, and washing machines, and the minerals create buildup in water heaters, coffee makes, and in cookware. The main disadvantage is these deposits, which can be hard to remove completely.
Hard water has health benefits, because it provides minerals that we need to have in our diet. You can use a water softener in your house, but these need to be used carefully because many of them remove the hardness by a process called ion-exchange, which results in putting large amounts of sodium into the water instead; excess sodium consumption is not healthy, and can contribute to high blood pressure.