Eukaryotic cells are structurally more complex than prokaryotic cells, and this complexity is largely due to the appearance of discrete membrane-bound compartments in which various cellular processes are compartmentalized. In most prokaryotes, cellular processes occur within one compartment.
The available data indicate that two major evolutionary processes have contributed to the complexity of eukaryotic cells. First, it appears that the plasma membrane has undergone various modifications. These invaginations have resulted in complex intracellular compartments such as lysosomes, the endoplasmic reticulum, and golgi apparatuses. The majority of DNA is found within a membrane-bound nucleus. Second, the mitochondria seem to be of prokaryotic origin. There is compelling data to indicate that during the early evolution of eukaryotes, an intimate association occurred between a primitive prokaryote and a primitive eukaryote. This intracellular symbiosis became permanent over the course of time, and what exists today is a stable remnant of that ancient association.
Here is a quote by Lewis Thomas from his classic book of essays, The Lives of a Cell, which puts these facts in a provocative context:
A good case can be made for our nonexistence as entities. We are not made up, as we had always supposed, of successively enriched packets of our own parts. We are shared, rented, occupied. At the interior of our cells, driving them, providing the oxidative energy that sends us out for the improvement of each shining day, are the mitochondria, and in a strict sense, they are not ours. They turn out to be little separate creatures, the colonial posterity of migrant prokaryocytes, probably primitive bacteria that swam into ancestral precursors of our eukaryotic cells and stayed there. Ever since, they have maintained themselves and their ways, replicating in their own fashion, privately, with their own DNA and RNA quite different from ours. They are as much symbionts as the rhizobial bacteria in the roots of beans. Without them, we would not move a muscle, drum a finger, think a thought.