Before we start, lets decide what it means for something to be clean. Lets say that by clean, we mean safe to drink. Some of the impurities that can be found in water include chlorine, lead and asbestos from old pipes, and bacteria and the amount of these impurities depends on where you get the water.

Water that is found outside in places like lakes and ponds has a lot of bacteria in it, which can make you sick. In order to kill this bacteria, the people in charge of making water safe to drink add chlorine (its also used in swimming pools, though the weird smell comes when there's not enough chlorine). If your water is provided by the city, there's a small amount of chlorine in the water that comes out of your faucet at home.

Even though chlorine is put in water to make it safer to drink, it can produce things that are harmful, and that smell and taste bad. Most of the water filters that you can find at the store are good at removing chlorine and the bad things it produces by using something called activated carbon. Activated carbon is basically charcoal with a bunch of tiny holes in it. This is how it works.

When you pass water with chlorine through activated carbon, the chlorine would much rather grab on to the carbon than stay in the water. This process of sticking is known as adsorption, and the tiny holes in the activated carbon provide more places for the chlorine to stick, which leads to cleaner water. Activated carbon is also good at adsorbing things other than chlorine, and doctors use it to treat people who've consumed certain poisons. Unfortunately, activated carbon doesn't kill bacteria , and once its fully covered by adsorbed impurities, it stops working! Though it is best to use water that is been cleaned by the city, in an emergency you can boil rain water, or water from lakes, ponds, or rivers. Boiling water for several minutes will kill most of the bacteria. However, other impurities such as metals and other chemicals may still remain. These can be removed through distillation.

In distillation, the water vapor from the boiling water is collected, cooled, and turned back into a liquid in a separate clean container.

I hope this helps answer your question. Here is a good online resource I used, and I recommend it in case you'd like to learn more:
activated charcoal