What characteristic defines eukaryotic organisms?

Eukaryotic organisms are distinctly characterized by the presence of a nucleus. This defining feature sets them apart from prokaryotic organisms, which do not contain a nucleus. In eukaryotic cells, the nucleus serves as the control center, housing the cell's genetic material (DNA) and regulating various cellular activities, including growth, metabolism, and reproduction. The compartmentalization provided by the nucleus allows for more complex cellular processes and organization compared to prokaryotes, which often have a more simplistic structure without membrane-bound organelles.

While eukaryotic cells indeed have a cell membrane, and although some may debate the complexity and size in terms of cell structure, these characteristics do not uniquely define eukaryotes as the presence of a nucleus does. The nucleus is essential for the characteristic traits and functions observed in eukaryotic cells.