Spiral galaxies are flat, rotating disks of stars, gas and dust, surrounding a prominent bulge of much older stars. The bulge/disk region is surrounded by a much fainter halo of stars, many of which reside in globular clusters. Around half the galaxies we can observe are spiral galaxies.
Spirals are so named because of the spiral structures (or arms) that extend out from the central bulge into the disk. These lumpy features are the sites of ongoing star formation, and are brighter than the surrounding disk because of the young, hot, blue stars that live within them.
Because spiral galaxies still have significant amounts of gas and dust, they are thought to be relatively young in comparison to elliptical galaxies. In fact, many astronomers believe that over time, spiral galaxies will evolve into ellipticals.
Spiral galaxies are mostly found in low-density regions of the Universe (i.e. with not many other galaxies nearby) and it is rare to find them in the middle of galaxy clusters. Our own galaxy, the Milky Way, is thought to be a spiral galaxy with a central bar feature.