In the beginning, there were "platform pedals" - pedals with no way to really secure your feet to the pedals. This is what I grew up with.

Later on, "toe clips" became the "in thing". It's sort of a "cage" on the pedal that you slide your foot into. These were a big improvement because you were able to apply pressure all around the 360 degrees (i.e., "pulling up as well as "mashing down").

"Clipless pedals" were a refinement of this - I think of them as somewhat similar to ski bindings. The pedal has a receiving device, into which your shoe with a "cleat" attached fits. It clicks in. Once in, you are very securely attached to the pedals (it is common when first getting these, to forget to unclip when stopping, and falling over as a result).

SPD (I think Shimano started this) was one of the first and still the predominant standard. "LOOK" is another one.

The next innovation was pedals with "float" - the ability to pivot horizontally as well as vertically. My SPD pedals don't have much float to speak of so my knee flexes up and down, but this is not a problem for me; people with bad knees or injuries, etc. often work very well with these types of pedals with the extra float. It depends on your individual requirements.

Stop by your local bike shop and check out the displays - you'll get a pretty good idea once you see these things up close.

Okay - that exhausts my knowledge!