Prokaryote is a simple cell without a nucleus or other membrane-bound organelles. Eukaryote is an organism with membrane-bound organelles, most notably the nucleus, and DNA linked to histone proteins.
Prokarytic cells reproduce by dividing equally by fission, or unequally by budding.
Eukaryotic cells normally reproduce by mitosis, a process that includes nuclear replication. Hence mitotic division produces two identical daughter nuclei. Mitosis in an eukaryotic cell is usually followed by cell division. Please refer to any biology textbook for further information.