The type of organism that has a nucleus and membrane-bound organelles is called a eukaryote. Eukaryotic cells, which include those of plants, animals, fungi, and protists, are characterized by their complex structure. The presence of a defined nucleus houses the cell's genetic material, while membrane-bound organelles, such as mitochondria, endoplasmic reticulum, and golgi apparatus, enable specialized functions. This organization allows for greater cellular efficiency and complexity compared to prokaryotes, which lack these features.