Cement, which is the abbreviation of the correct name, "Portland cement" is a fine grey powder which looks very much like grey flour. Most people have never seen cement. Concrete is a mixture of cement, sand, rock, water and small amounts of additives. Concrete is the material we encounter in our everyday lives.
The relationship between cement and concrete is similar to the relationship between flour and cake. While neither cake nor concrete can be made without the "flour" they are definitely not flour and like a cake, when the concrete has finished "cooking", the flour is nowhere to be seen.

Another way to think about it is that; cement is the glue in the concrete holding the sand and stone together. It should also be noted that like a lot of glues, cement doesn't "dry"; it hardens through a process called hydration.