A Eukaryote can be thought of in evolutionary terms as the “Cell Mk II”, the Prokaryote being the “Mk I”. The main difference between a Eukaryote and a Prokaryote is the presence of large Organelles such as Endoplasmic Reticulum, Golgi Apparatus, Nucleus, Mitochondria, Chloroplasts, and Lysosomes. Organelles allow cellular reactions to take place in a contained area where the optimum conditions for such reactions could be maintained, in Prokaryotes these reactions took place in the cell cytoplasm, which was less efficient. It is thought that organelles were once prokaryotic organisms that evolved a mutualistic relationship with the Eukaryote.
Being eukaryotic is a prerequisite to being multi-cellular. All animals, plants and fungi are eukaryotic, as organisms of their complexity cannot exist without using specialised organelles. There are many single-celled Eukaryotes, for example yeast.
Upon the subject of Ribosomes - there seems to be some debate about these in the Prokaryote, and Organelle node. Prokaryotic Ribosomes are slightly smaller than Eukaryotic Ribosomes, but are still classified as organelles.