When talking about bicycle pedals, there are basically two types; flat pedals which is a standard metal platform spinning round the axle and suitable for any kind of shoe; and clip in (more commonly known as clipless pedals from previous years when racing pedals used to have a toe clip on them) where the shoe is actually clipped in to the pedal via a cleat in on the bottom of a specialist cycling shoe just like ski bindings.
Flat pedals are ideal when you just want to go out for a spin and do not need specialist cycling shoes but the power transfer between shoe and pedal is not very efficient which is why people move on to clipless pedals when they start to do more cycling.
Clipless pedals come in various shapes and sizes but all involve a special cleat on the bottom of a cycling shoe which locks the shoe on to the pedal but fear not as they all have a quick release system built in where you just have to twist your foot sideways to disengage the shoe from the pedal. The is also a certain amount of float or travel built into clipless pedals or cleats which allows the foot to move a certain distance before starting to disengage, this is better for those prone to knee problems as they are not fixed into just one position when cycling. The amount of float available depends on the brand of pedal but most manufacturers offer a tuneable amount of release tension on the pedal even if float is fixed so best to check each system against your needs before buying. It is worth bearing in mind that clipless pedals only work with specialist cycling shoes so you will need to factor in the additional cost of cycling shoes when buying these types of pedal.