What is characterized by a single, membrane-bound organelle that contains genetic material?

A eukaryotic cell is characterized by the presence of a true nucleus, which is a membrane-bound organelle that contains the genetic material (DNA). This differentiation from prokaryotic cells is significant because prokaryotes lack a nucleus and their DNA is instead located in a region called the nucleoid, which is not surrounded by a membrane.

Eukaryotic cells can be found in a wide variety of organisms, including animals, plants, and fungi, which means that the features of eukaryotic cells are broad and encompass various specific types of cells. While fungal and plant cells are indeed specific types of eukaryotic cells, the question asks for a general category, which is best described by the term "eukaryotic cell."

In summary, the defining characteristic of eukaryotic cells is that they possess a nucleus as a membrane-bound organelle, setting them apart from other cellular types like prokaryotes.