Clipless pedals (also known as clip-in or step-in) require a special cycling shoe
with a cleat fitted to the sole that interfaces with a locking mechanism on the pedal. The term "clipless" used for this type of pedal actually means that it doesn't need to use an external toe clip.
The primary benefits that clipless pedals offer the rider are:
1) The rider always has the ball of their foot on the pedal where the most power can be transferred. Often, newer riders will be pedaling with the pedal resting in the arch of their foot, which causes health problems for the rider with long term use and doesn't provide the rider the ability to fully extend their foot (with their calf muscle), thereby forfeiting a healthy percentage of power they could be generating.
2) With clipless pedals, a rider can power their bike by both their upstroke and downstroke. This gives the rider a significant advantage on uphill rides.
3) Being connected to the bike gives the rider increased maneuverability. Bunny hops are easier, leaning the bike is easier, and balancing your weight on the pedals is easier.
Clipless Pedals w/ No Platform
This is one type of clipless pedal. Their biggest benefit is that they are lightweight. The Shimano SPD pedal pictured below is one of the most popular because of its low weight and ability to shed mud.
Clipless Pedals w/ Platforms
Some riders would rather have a wider platform to push down on rather than have a smaller pedal, so there are plenty of clipless pedals like the one pictured below (Crank Brothers Mallet M) that meet that need.
Platform pedals refer to any flat pedal (typically for mountain biking and BMX) without a cage. MTB
and BMX riders alike prefer platforms to cage pedals because they are rounder, they offer more grip using short metal studs, and they do less damage to a rider's shins and ankles during an accident (cage pedals will often scrape skin off the shin if the rider stops short and loses footing of the pedal).
More expensive platform pedals for the mountain bike
market are available with replaceable metal traction pins and cartridge bearings. In recent years, lightweight pedals intended for freeride and downhill
cycling have been made from exotic alloys such as magnesium.
The majority of MTB
and BMX riders do not install toe clips on this kind of pedal because bailing from a toe clip in an emergency situation is often more difficult then bailing from a clipless pedal.
Caged pedals are pedals that can accommodate toe clips, not necessarily the clips that go on the pedal and over the toe (which many people confuse for "cages"). The actual cage is the outer part of a conventional pedal, the part that comes into contact with the rider's shoe and has holes where toe clips can be secured by screws.
Cage pedals built for mountain biking are typically serrated so that even when muddied, the pedals can be gripped well by any flat shoe.