Kitchen water filtering systems range from under the sink to refrigerator filters dispensing water and ice from the door. There are countertop steam distilling units, and pitcher units with replaceable cartridges. They all have their benefits and drawbacks.
Under the sink models connect to the cold water line and filter the water before it gets to the faucet. They use activated carbon, much like the faucet mounted filter systems. Those connect to the faucet itself, and have an on demand feature to direct the water to the filter when you want it to be. It is best not to run hot water through these filters. With a pitcher unit, you fill it from the tap, and it is gravity fed through a carbon filter. These all require replacement of cartridges periodically, as does the refrigerator filter.
For countertop models of a home steam distiller, they use your tap water like the pitcher unit. The water is brought to a boil, and there are special vents to release inert gases and impurities that have a lower boiling point than the water. The water boils and becomes steam, which is collected and recondensed to liquid. The results are distilled, clean water, with the deposits and solids remaining in the vessel used to boil the water, to be washed away before the next use. No matter what type of kitchen water filtering system you decide on, they all need to be maintained to ensure the longevity of the unit and the quality of the water you get out of it.