Sebastian M. answered 12/02/19
Neuroscience graduate w/ experience tutoring high school students
Hi there Sam!
The prokaryotic cell is the most simple of these two. You may recall that, unlike eukaryotes, prokaryotic cells do not have membrane-bound organelles. Their genome, composed of double-stranded DNA, is just floating in the cytoplasm in the shape of a circle; we call this the nucleoid.
Eukaryotic cells, on the other hand, have membrane-bound organelles. This means that DNA can be stored elsewhere, perhaps to protect the genetic information or to make it easier to find (like storing your socks in one dresser). Most of the eukaryotic genome is stored in the nucleus, and it is found in the vast majority of eukaryotic cells*. The rest of the DNA can be found in the mitochondria, another membrane-bound organelle which is responsible for cellular respiration (that is, the process of making ATP for energy).
If you're having trouble remembering that small fraction of mitochondrial DNA that exists independently of the nucleus, familiarize yourself with the endosymbiotic theory. To summarize, scientists think the mitochondria was a cell of its own, complete with its own genome, which one day entered symbiosis with a larger host cell. A symbiotic relationship means that each player (the mitochondria and the host cell) benefit from it (unlike a parasitic relationship). Knowing this, we can recognize that there ought to be two locations of DNA in the modern-day eukaryotic cell, as opposed to one in the prokaryotic cell.
Hope this helps! Would be glad to explain this in simpler or more advanced terms if necessary.
* If you're curious, mature red blood cells get rid of nuclei to make space for hemoglobin and thus, oxygen. What this means is that the cells cannot reproduce, and therefore, when they reach the end of their lifespan, they're recycled for their parts.