Why isolated, recombinant plasmid DNA without any restriction is often detected in agarose gel electrophoresis as three DNA bands?
These are the three forms of the plasmid: supercoiled (smallest 3D-structure, runs fastest), linear (runs in the middle) and relaxed, nicked plasmid (runs highest). You can have another fourth band, which is the circular single stranded plasmid (runs faster than the supercoiled version). See the following figure (from this article, which I recommend reading):