There are a couple of setups out there. One is a "ram air" style and the other is "cold air" setup. Mostly everyone calls any cone filter and cheap China pipe a CAI.
The ram air intake is basically a small length of tube with a cone filter that eliminates the stock airbox. Various models of various manufactures for cars have more restrictive stock airboxes so there can be some small gains in running a ram air. The cons to a ram air is that by eliminating the stock box, youre now sucking up hot engine bay air. You can gain some power due to a less restrictive path for airflow, but the heat can screw you.
The cold air setup is usually a longer tube that sticks the filter directly in the path of fresh, cold air. It can be to a headlight funnel, naca duct, or a lower section of fender well. The colder air is more dense which packs more oxygen into the chamber producing higher HP numbers. Numbers will fluctuate with outside temps and with whatever setup youre running. The problem with those, is your filter is usually exposed to the elements which can result in sucking up water during heavy rains or if youre driving though puddles.