The main reason people fit an induction kit is to get the lovely deep sound that is muffled by the air box. In high performance engines and turbo engines you may also see slight power gains at the top end.
Simply adding an induction kit will allow the car to suck in air more freely. Induction kits usually consist of a cone or hemispherical filter with no air box. This is to allow more air to enter the engine. The standard paper filters that car have in their air boxes can be very restrictive to airflow.
Performance filters needs to compromise between filtration and the drag they cause. They are generally made from foam, gauze, cotton or a mixture of the three. Cotton filters give the best filtration to reduced drag.
Oil is generally used to aid the filtration as it traps the small particles of dirt instead of allowing them to flow into the engine.
Induction kits should not be confused with performance air filters. The latter fit in the OEM intake box and are swap in replacements. An induction kit replaces the air box and is generally a cone, cylinder or hemisphere shape. Good induction kits include a cold air feed.