Cleat is the piece of metal permanently attached to the sole of the shoe with a couple of screws. When you get on the bike, you aim your shoe so that the cleat fits into pedal's binding mechanism (you hear an audible "click" when it binds).

I ride in temperatures anywhere from -30C to +30C and I do not like to be attached to the bike in winter conditions. So I bought a cheap SPD compatible pedal (by Wellgo) that has binding mechanism only on one side. The other side of the pedal is normal platform. Then I bought a pair of biking shoes that came with SPD cleats (I had to install the cleats myself, but that's easy). Now I can ride with bike shoes and click in, or use normal footwear and platform side of the pedal. I've been happy with this setup.

--J