The largest organelle in a eukaryotic cell is the nucleus. It serves as the control center, housing the cell's genetic material in the form of DNA. The nucleus is surrounded by a double membrane known as the nuclear envelope, which allows for selective transport of molecules in and out of the nucleus, thereby regulating gene expression and cell function. The presence of a distinct nucleus is a defining characteristic of eukaryotic cells, differentiating them from prokaryotic cells, which lack such organelles and have their genetic material freely floating in cytoplasm.