Eukaryotic cells differ from prokaryotic cells in a number of ways, notably in size, complexity and cooperative behavior. The division between eukaryotes and prokaryotes is the deepest divide in nature, with two domains of life classed as prokaryotic and just one group of eukaryotes.
All animal, plant, fungal and protist cells are eukaryotic. Their genetic material is contained in a discreet nucleus, and they have identifiable organelles and other structures in their cytoplasm. Eukaryotes also tend to be many times larger than prokaryotes. Prokaryotic cells lack a nucleus and organelles, and their genetic material consists of a single ring-shaped chromosome rather than the multiple linear chromosomes of the eukaryote. Prokaryotic cell walls lack transport proteins and other structures useful for signaling.
Behaviorally, the two types of cells are very different. Prokaryotic organisms reproduce by a process known as conjugation, whereby two cells simply pass each other some genetic material that was floating free in the cell. Eukaryotic organisms reproduce via meiosis, which is a much more complicated form of cell division that separates the entire DNA strand and passes half of it along to offspring.
Another major difference between the two types is the degree to which they work together. While some prokaryotes live communally, only the eukaryotes have evolved true multicellularity. All large organisms on Earth are eukaryotes, and all are more closely related to each other than any is to a prokaryote.