Actually, the stars and nebulae that make up the spiral arm are only temporarily part of that spiral arm. Spiral arms are more like sound waves where individual particles move around a more or less stationary position. (Look for instance at the animation of longitudinal waves from Dan Russel, the red dots move a bit to the left and to the right around a stationary position). Dust, gas and stars move towards or away from another just as longitudinal waves. Where the dust, gas and stars come close together (and where, therefore, the density increases), spiral arms can be seen as more stars are close together increasing the brightness at that position in the galaxy.
This effect is, furthermore, much increased because the increased density of dust and gas in the spiral arm causes protostars to form. The brightest stars burn up their energy so fast that they will cease to exist even before the longitudinal wave (the spiral arm) has passed. These very bright stars only exist for a small portion of their orbital period around the galaxy's centre, and only while they are in the spiral arm. The large majority of stars exist much longer, but are also much dimmer and contribute only little to the overal brightness of the galaxy.
This causes the spiral arms to be so much brighter than the rest of the disk, where also a lot of stars exist. But these can hardly be seen as they are much dimmer.
Of course, the stars do not revolve around a stable position in the galaxy (as the red dots in the wave animation) but follow their own orbits around the centre of the galaxy. Sometimes a bit faster, and sometimes a bit slower depending on the position relative to the spiral arms.
Because the spiral arms are waves, it does not matter that stars near the centre move faster than the stars at the edge. It just means that they will be part of the spiral arm for a shorter period of time.