Final answer:
Cells with membrane-bound organelles and a nucleus that stores DNA are called eukaryotic cells, which are found in animals, plants, and many unicellular organisms.
Step-by-step explanation:
The cells primarily found in animals and plants that have membrane-bound organelles, including the ability to store DNA in a nucleus, are called eukaryotic cells. Unlike prokaryotic cells, eukaryotic cells have a true nucleus where the DNA is surrounded by a membrane, and they also contain other membrane-bound organelles, such as mitochondria, the endoplasmic reticulum, and the Golgi apparatus, which allow for specialized functions. All multicellular organisms, including animals and plants, as well as many unicellular organisms, are made up of eukaryotic cells.