Eukaryote
A eukaryote is an organism whose cells contain a nucleus and membrane-bound organelles; plants, animals, fungi, and protists are eukaryotes.
Definition
A eukaryote is a living thing whose cells have a nucleus, a compartment that holds the DNA, along with other small parts called organelles that each do a job. Its cells contain a membrane-bound nucleus and membrane-bound organelles such as mitochondria, the endoplasmic reticulum, and, in plants, chloroplasts; eukaryotes may be unicellular like yeast and many protists or multicellular like plants and animals, and their DNA is organized into multiple linear chromosomes. Together they form the domain Eukarya, defined by a nuclear envelope with pores, an endomembrane system (endoplasmic reticulum, Golgi apparatus, lysosomes, vesicles), a cytoskeleton of actin filaments and microtubules, and mitochondria of endosymbiotic origin. Because transcription in the nucleus is separated from translation in the cytoplasm, RNA can be processed by splicing and capping before use. Cell division proceeds by mitosis or meiosis using a spindle apparatus.
Example
You are a eukaryote, and so are an oak tree, a mushroom, and the amoeba in a drop of pond water; all keep their DNA inside a nucleus. A human cheek cell is about $50\ \mu\text{m}$ across, ten to twenty times the diameter of a typical bacterium, and holds $46$ chromosomes in its nucleus, while a plant leaf cell adds a cell wall, a large central vacuole, and dozens of chloroplasts. The human genome contains about $3.1$ billion base pairs across $23$ pairs of chromosomes; stretched end to end, the DNA in one nucleus would be roughly $2\ \text{m}$ long, packed into a nucleus about $6\ \mu\text{m}$ in diameter by wrapping around histone proteins.
Key Insight
The word comes from Greek for "true kernel," because the nucleus looks like a seed in the middle of the cell. Compartments let a eukaryotic cell run many chemical reactions at once without interference, the way a school runs different classes in different rooms. The eukaryotic cell is best understood as a chimera: a host cell that acquired mitochondria, and later in plant lineages chloroplasts, from bacterial endosymbionts. Multicellular complexity became possible because that partnership provided a large, reliable energy supply per gene.