In a spiral galaxy, which is a flat, thin disk of gas and stars that undergoes 'differential rotation', material in the disk is subject to a gravitational instability which orbits the center of the galaxy at a specific 'pattern speed'. In some parts of the disk, the pattern speed equals the local orbit speed of material around the center, and at this 'co-rotation' radius, material never enters or leaves the vicinity of the pattern. At other locations, material enters the spiral pattern 2 times per orbit in a two-armed spiral.
The pattern itself, called the spiral density wave, is simply a region of space where the gravitational instability has briefly piled up more material than average elsewhere in the galaxy. This piling up of material causes objects like molecular clouds to assemble themselves into larger 'giant molecular clouds', and the process may be violent enough to trigger star formation. The stars that form are luminous and massive, and these stars then light up the material in their vicinity so that the locus of these stars across the galaxy at any one time shows where the spiral density wave has been. But by the time the stars form, the spiral pattern has moved onward and begun to assemble the next collection of clouds...etc.
The density wave is not a solid object, but is just the locus at any given time of where the gravitational instability in such a thin rotating disk has been able to assemble large clouds and star forming activity.