Agarwood, or oud, is wood harvested from Aquilaria trees that create a dark, aromatic resin in response to a fungal infection. Agarwood oil can be produced from the wood through steam distillation or by CO2 extraction. The end product has a deep, woody, earthy, animalic, resinous scent, though the nuances vary depending on the source and processing method. Oud is a very expensive ingredient because it is rare, and the supply has become even more limited because of overharvesting. Trees are now being cultivated for a sustainable supply.
Synthetic agarwood blends are also commonly used, and in fact most of the oud notes in mainstream perfumery are created with synthetics. These synthetic blends tend to be cleaner smelling than the real thing, with far lighter animalic notes. The synthetics still smell good, but they don’t smell the same as the natural. Oud as a note has become something of a fad in recent years.
Photo shows an agarwood tree, Aquilaria crassna, with some bark removed. From wiki, by Blaise Droz.