Nucleus
The nucleus is the membrane-bound organelle in eukaryotic cells that stores DNA and controls the cell's activities.
Definition
The nucleus is the control center of a cell, holding the DNA that tells the cell what to do and how to build everything it needs. It is a membrane-bound organelle of eukaryotic cells that contains the chromosomes, surrounded by a double membrane called the nuclear envelope whose pores let messenger RNA and proteins pass, and it directs cell activity by controlling which genes are transcribed; the nucleolus inside it makes ribosome parts. The envelope consists of two lipid bilayers continuous with the endoplasmic reticulum, perforated by nuclear pore complexes that gate the traffic of macromolecules. Inside, DNA is packaged with histones into chromatin, organized into chromosome territories, and transcribed into RNA that is capped, spliced, and polyadenylated before export. Separating transcription from translation permits extensive RNA processing and layered gene regulation that prokaryotes lack.
Example
In a stained cheek cell under a microscope, the nucleus shows up as a dark round spot near the middle, and that spot holds all $46$ of your chromosomes. A human nucleus is about $6\ \mu\text{m}$ in diameter and holds roughly $2\ \text{m}$ of DNA; when a protein is needed, its gene is copied into mRNA inside the nucleus and shipped through the nuclear pores to ribosomes. A nuclear pore complex has a mass of about $120$ megadaltons and can pass around $1{,}000$ molecules per second, and proteins larger than roughly $40\ \text{kDa}$ need a nuclear localization signal recognized by importin proteins to enter.
Key Insight
The nucleus does not do the building itself; it is more like a library of blueprints, and copies of the plans are sent out to the rest of the cell. Mammalian red blood cells lose their nucleus as they mature, which is why they cannot repair themselves and live only about $120$ days. Because most somatic cells carry a complete genome in the nucleus, a differentiated cell's identity depends on which genes are switched on, not on which genes it has. Cloning by nuclear transfer proved this by producing a whole animal from a single adult nucleus.