Clone (verb) is the action of duplicating the genetic material within a vector. To clone the piece of DNA, one would insert it into some type of the vector (like, a plasmid) and put the resultant construct into a host (generally a bacterium) so that the plasmid and insert replicate with the host. An individual bacterium is made isolated and grown and the plasmid containing the "cloned" DNA is re-isolated from bacteria, at which point there will be many millions of copies of the DNA - essentially an limitless supply. Actually, an investigator wishing to clone some gene or cDNA rarely has that DNA in a purified form, so practically speaking, to "clone" something involves screening a cDNA or genomic library for the desired clone. See also "Probe" for a description of how one might start a cloning project, and "Screening" for how the probe in used.
One can also clone more complex organisms, with considerable difficulty. The much-publicized Scottish research that resulted in the sheep 'Dolly' exemplifies this approach.