Supercoiling is a property of DNA in which the DNA becomes tightly twisted around itself, compacting it into a much smaller space. A circular bacterial chromosome in vivo, for example, would be tightly supercoiled. If that same chromosome had no supercoiling, it would be one large relaxed circle. Therefore, the supercoiled chromosome would take up much less space in the cell compared to a relaxed chromosome even though they contain an identical amount of base pairs.
Consider the following electrophoresis gel. Recall that smaller lengths of DNA migrate faster through an electrophoresis gel than longer ones.
Each lane contains the same circular sequence of DNA, identical in both length and sequence. However, each DNA sample is under a different level of supercoiling.