Why do some cellular organelles like mitochondria and plastids have their own DNA. And what is the basic difference between the DNA of the nucleus and these organelles?
Mitochondria and plastids are the result of two ancient mergers. A kind of symbiotic relationship where one cell phogocytized another. Rather than being digested, the phagocytized cell, complete with its own DNA cooperated with the cell that "ate" it. This was part of the evolution of eukaryotes. This idea is called endosymbiosis, and was championed by Lynn Margulis in the late 1960s. Mitochondria and plastids come from Bacteria, and carry the traces of their original DNA. However, a complete genome was no longer required for the new function, so mitochondria lost many redundant genes. Mitochondrial genomes are much smaller. Plastid genomes are larger than mitochondrial genomes, but smaller than the genomes from which they originated.