An initial question might be why eukaryotic cells arose. One important thing that changed in the world about the time that the first eukaryotic fossils appear is that the atmosphere of the planet was beginning to fill up with free oxygen, almost certainly due to the increasing numbers of photosynthesizing organisms in the world. Oxydation chemistry tends to release energy. So we're pretty sure that it was about this time than aerobic cellular respiration arose. The overwhelming difference between anaerobic cellular respiration and aerobic cellular respiration is the amount of energy produced by the two processes.
Aerobic respiration produces many times more energy than anaerobic respiration does.
Hypothetically, this increase in available energy was at least part of what promoted the development of the much larger and more complex eukaryotic cell. The probable answer is that there were at least two different kinds of events that added to the complexity of cell structure. Many of the structures in eukaryotic cells probably developed from the elaboration of the membranes of the cell. This is the likely explanation for the origin of the endoplasmic reticulum, golgi apparatus, and nuclear envelope. But the evidence strongly suggests a much more interesting origin for the two great energy processing organelles, the mitochondrion and the chloroplast.