Drip brewing, or filtered coffee, is a method which involves pouring water over roasted, ground coffee beans contained in a filter, creating the beverage called coffee. Water seeps through the ground coffee, absorbing its oils and essences, solely under gravity, then passes through the bottom of the filter.
In this style of brewing, ground coffee is fully immersed in hot water for all or most of the brew, and then filtered at the end (think steeping tea). The previously mentioned French Press is full immersion. Full immersion tends to produce good body and depth to the cup, and is consistent and easy.
The concept behind the pour over consists of hot water being poured over a bed of coffee grounds. The water is constantly flowing through the coffee grounds for continual extraction. There are many types of pour overs on the market. Cloth or paper filters can be used depending on your taste preference.