The oldest and most common types of faucets are compression faucets. When one of these faucets is in the off position, a small washer inside creates a seal that keeps water from flowing through and into the tap. But when you turn the faucet on, the stem inside raises up, which takes the pressure off of the washer and breaks the seal. That allows the water to flow until you lower the stem back down again by turning the faucet off.
These faucets are generally easy to find and relatively cheap. They are also easy to install or repair on your own, and this is fortunate because they do tend to develop leaks periodically. That is primarily because the washer inside will wear out over time and need to be replaced. This is a rather straightforward and simple process, but if you do not want to have to deal with it, you may want to consider your other option.
The other main type of faucet on the market today is a cartridge faucet. Instead of washers, these types of faucets employ a cartridge which seals to the faucet base with several O-rings. These types of faucets can often be quite a bit more expensive, although you can certainly find some that are reasonably priced. They are also much less prone to developing leaks, and when they do they are quite easy to repair as well.