A podded engine is a jet engine in a pod, typically attached below the wing or to the tail of the aircraft. The pod itself is called a nacelle.
Placing engines on the wing provides beneficial wing bending relief in flight. Early British jet aircraft had their engines buried in the wing root. See the de Havilland Comet, the V bombers and the Hawker Siddeley Nimrod. The further the engines are away from the fuselage the greater the wing bending relief so engines buried in the wing root provide little relief. Almost all modern large jet airplanes use engines in pods located a significant distance from the wing root for substantial wing bending relief. The pods are in front of the wing to help avoid flutter of the wing which, in turn, allows a much lighter wing structure. Locating the pod below the wing provides each engine with air undisturbed by the fuselage or wing. The wing also blocks some engine noise from reaching the aircraft cabin.
Smaller jet airplanes which are not suited to podded engines below the wing because they would be too close to the ground commonly have two podded engines located at the rear of the fuselage. For example, see the Cessna Citation. This mounting location provides no wing bending relief but, following an engine failure, does have much less asymmetric thrust than a wing-mounted engine. Careful examination of such engines will show them typically mounted nose-high. These engines are mounted to face the local flow of air, and the local airflow at the airplane's tail is descending.
As unusual counter-examples, the VFW-614 and the Hondajet place the podded engines above the wings. The Antonov An-72 and the Boeing YC-14 also place their engines above the wings, mounted very close to the wing. This placement utilizes the Coandă effect allowing a lower minimum flight speed and decreasing the amount of runway needed for takeoff and landing (i.e. STOL).
Modern jet fighters almost never use podded engines, instead typically embedding the engines within the fuselage. This was not true of earlier designs, however. The Messerschmitt Me 262, for example, used under-wing pod mounted engines. The Bell P-59 Airacomet used engines mounted in pods tucked up against the fuselage.