Sold as a pair, bicycle pedals thread in to the crank arms and are the point of contact to propel the bike from. Three major categories of pedals exist - clipless, platform and clip.
Pedal compatibility is near universal, with nearly all adult bikes needing pedals with a 9/16" thread. Some cheaper bikes and kids bikes need a 1/2" thread. If not noted, assume the pedals are 9/16" thread.
Commonly found on BMX, urban and mountain bikes, platform pedals let you simply step on and start riding. Unlike, for example clipless pedals, these are the easiest type of pedal to use and do not call for any special technique when it comes to putting the foot on or off the pedal. More expensive platform pedals offer greater strength, better bearings and better traction.
Used in conjunction with cycling shoes which hold the 'cleat', clipless pedals allow you to mechanically attach your foot to the pedal. Similar in design to that of a ski binding, clipless pedals are confusingly named as such as they are free from the old fashioned 'toe clips'. Clipless pedals are near standard equipment on road bikes and higher-end mountain bikes. Due to the attached nature of the system, they require some practice as it's possible topple over while still attached to the bike.
Mounted to the shoe, the cleat locks into the pedal which holds the shoe firmly to the pedal, a small side twist of the foot releases the shoe from the pedal. The benefits to clipless pedals are the efficient transfer of pedaling power and being connected to the bike.
Clipless pedals are typically split into two categories: mountain bike and road. Mountain bike clipless pedals use a two-hole cleat, feature two or more sides and are built to clear mud. Due to the smaller cleat, shoes designed for mountain bike pedals are easier to walk in and so make a better choice for commuters and recreational cyclists too.
Road clipless pedals typically use a three or four-hole cleat, are often one-sided and built with a larger surface area for greater power transfer. The larger cleat can be awkward to walk in.
Combination pedals are convenient for riders who wish to be able to clip in but also ride in normal shoes. These are versatile pedals which have a platform style on one side and clip in on the other. They're popular for commuting use, but the one-sided clip nature can be frustrating for users that always ride clipped in.
Toe clip pedals attach the foot to the pedal via a cage and strap. Now considered an older and less popular option to clipless pedals, toe clip pedals still allow the foot to be attached to the bike without the need for special cycling shoes. Toe clip pedals are considered less safe than clipless versions given that the shoe can become trapped in emergencies. For this, toe clip pedals are not recommended for mountain biking.