A common piece of equipment in a chemistry laboratory. Basically, a Büchner funnel is a funnel, usually made out of ceramic or hard plastic, with a large cylindrical bowl and fairly short (~5 cm) stem. The funnel should also have a rubber stopper where the stem connects to the bowl. While conventional funnels merely allow liquids to flow freely into a small-necked container, Büchner funnels have a perforated disk at the bottom of the bowl.
To use a Büchner funnel, you need a specialized Erlenmeyer flask with a glass tube about 2 cm long sticking in the neck. Use a rubber tube to connect this tube to a vacuum pump or an aspirator. The funnel goes in the neck of the flask. The rubber stopper ensures that when the suction is engaged, the only way that air can get through is through the funnel. A round piece of filter paper goes in the bowl so that large particles are caught by the filter paper instead of going through the perforations in the funnel. The idea is that when the aspirator or vacuum pump is turned on, it will create low pressure in the flask, so anything poured into the funnel will get sucked into the flask. Hopefully, the stem of the funnel reaches past the tube where the vacuum pump connects, so that fluid sucked through the flask doesn't go down the tube connected to the vacuum pump. This is why it's useful to have a reservoir between the flask and the pump.
A common usage of a Büchner funnel is when you have a solid/liquid mixture and you want to separate the solids from the liquid. Most commonly, you will have mixed two liquids and a solid will precipitate out, and you are only interested in the solid or the liquid, so the two must be separated.
Distinguished noder anuerin tells us that the funnel was named after Eduard Büchner, winner of 1907 Nobel Prize for Chemistry.