What is the difference between a prokaryote and a eukaryote?

Prokaryotic cells are cells that do not have a true nucleus, they are not organized so their DNA is not packed within a nucleus its free roaming within the cell. prokaryotic DNA is also Shorter than eukaryotic DNA.
Prokaryote examples: bacteria, protazoans etc.

Eukaryotic Cells: they are cells that have a true nucleus, they are highly organized, and they have systems which are organelles like smooth and rough ER, Nucleolus, nucleus, cell membrane etc. If you think about it as a human body part. each of those systems have a purpose. For instance, the cell membrane allows the cell to remain intact from outside interference, or in the nucleus, the dna replication happens. etc.

this is just a basic if you want a more detailed explanation (like biochemistry) then I can do that for you.

here is a more basic explanation of it.

http://animals.about.com/od/animalswildlife101/a/diffprokareukar.htm

Below this thread, you'll see a "related topics" block. This question has been asked plenty of times before, so perhaps you could find an answer there. If not, just let us know, and we'll explain it a little bit better.