It should be very obvious that a filter with a larger surface area will provide more airflow than one with a smaller airflow. Couple that with a larger opening for air to get into the airbox and an intake hose/pipe with a smoother internal surface as compared to the stock pipe. Then add in the weight difference and factor in the difference in thermal conductivity between materials (plastic vs aluminum vs carbon fibre). Those small differences add up to produce measurable differences.
A CAI or an IC won't "make" horsepower or torque. They make the engine more efficient. The engine produces the same amount of energy either way. The upgraded parts are more efficient, and therefore less energy is "lost" or "wasted" due to drag, temp, velocity, etc.
Think of it like trying to breathe through a straw vs a paper towel tube. You'll get enough air to live on either way, but it's much easier to breathe through the tube because the tube is less restrictive than the straw is. The same concept applies to the intake on a car. It will take less energy to suck air through a less restrictive intake than a restrictive one. That energy can then go to the wheels instead of being used to suck in air.
On top of that, more air can pass through the intake system since it is less restrictive. Since the engine can get more air in, it can add more fuel and make more power.
Carbon fibre intakes aren't really meant for people making a "budget" build or people who want something that's "good enough". Two main types of people buy them: people who are chasing performance/efficiency and people who are chasing looks/appearance.