Eukaryota is a taxonomic term referring to the domain containing all species with eukaryotic cells - that is, cells with membrane-bound nuclei. This is distinct from prokaryotic creatures, which fall under the domains Bacteria and Archaea.
In general, eukaryotic cells are structured in a much more complex manner than prokaroytic cells. These are the cells you studied in high school biology, with the endoplasmic reticulum, mitochondria, and chromosomes bunched within.
The Eukaroyta domain contains virtually all multicellular life on this planet. This includes the kingdoms Animalia (animals), Plantae (Plants), Fungi, and Protista (protists such as algae and protozoa). It is believed that first eukaryotes evolved on Earth around 2-3 billion years ago, though much debate ensues on when the first protists began taking form.