DNA supercoiling is important for DNA packaging within all cells.  Because the length of DNA can be thousands of times that of a cell, packaging this genetic material into the cell or nucleus (in eukaryotes) is a difficult feat.  Supercoiling of DNA reduces the space and allows for DNA to be packaged. In prokaryotes, plectonemic supercoils are predominant, because of the circular chromosome and relatively small amount of genetic material.  In eukaryotes, DNA supercoiling exists on many levels of both plectonemic and solenoidal supercoils, with the solenoidal supercoiling proving most effective in compacting the DNA.  Solenoidal supercoiling is achieved with histones to form a 10 nm fiber.  This fiber is further coiled into a 30 nm fiber, and further coiled upon itself numerous times more.
DNA packaging is greatly increased during mitosis when duplicated sister DNAs are segregated into daughter cells.  It has been shown that condensin, a large protein complex that plays a central role in mitotic chromosome assembly, induces positive supercoils in an ATP hydrolysis-dependent manner in vitro. Supercoiling could also play an important role during interphase in the formation and maintenance of topologically associating domains (TADs).
Supercoiling is also required for DNA/RNA synthesis.  Because DNA must be unwound for DNA/RNA polymerase action, supercoils will result.  The region ahead of the polymerase complex will be unwound; this stress is compensated with positive supercoils ahead of the complex.  Behind the complex, DNA is rewound and there will be compensatory negative supercoils. Topoisomerases such as DNA gyrase (Type II Topoisomerase) play a role in relieving some of the stress during DNA/RNA synthesis.