Other forms: nuclei; nucleuses
A nucleus is often called the brain, or control center, of a eukaryotic cell (that is, a cell with a nucleus).
The noun nucleus has several senses, though most of them will appear in science. If a biology teacher says nucleus, she is probably talking about a cell (or a group of cells), but a physics teacher would be talking about the center of an atom, or possibly even the center of a comet’s head. Step out of science class, and nucleus likely refers to a core group — like the math fanatics that math club could not function without.