Often, the most interesting things in astronomy happen unexpectedly. A few days ago, Comet Holmes was an extremely faint comet invisible to all but the largest amateur telescopes, slowly circling the sun between Mars and Jupiter. Then, in the early hours of Wednesday morning, Henriquez Santana in the Canary Islands discovered that the comet had brightened by a factor of nearly 25,000 -- invisible to the eye, but easily visible in even small binoculars. And, within a day, it had brightened further -- to third magnitude -- visible to the naked eye, even in the glare of the full moon. All-in-all, Comet Holmes is a million times brighter than it was a few days ago.
First, remember what a comet is -- comets are a few miles across, a loose, "dirty snowball" of dust and ice loosely packed together. Far from the sun, everything remains frozen, and the comets are very faint, because they are small. When comets come close to the sun, they warm up, the ice starts to melt, and the comet jets gas and dust out into space. The gas emits light like a neon lamp, and the dust reflects sunlight, so we can see the comet's typical head and tail from the Earth.
Because comets are so loosely packed, they can split into multiple pieces, shed large chunks, and even completely disintegrate. Usually this happens when the comet is close to the sun (and feeling stressed by the build-up of pressure from melting ice and gas) or when the comet is very near a planet or the sun, when gravity helps to rip it apart. But, sometimes, the comet just spontaneously breaks apart or sheds a lot of matter. This seems to be what happened with Comet Holmes.
Comet Holmes had a similar outburst over 100 years ago, in 1892. So, for some reason, this comet seems to be prone to either breaking apart or suddenly shedding dust. Perhaps, if we can better understand this comet, we can understand how comets formed, and how we might protect ourselves if a comet were ever to be discovered coming this way.
Do you want to see Comet Holmes? First, you need to live in the Northern Hemisphere. For now, you can still see it with your unaided eye, though binoculars will help, especially if you live in a city. The comet is in the constellation Perseus, which is up all night this time of year. Star charts like those found at Sky & Telescope are probably necessary, especially if you don't know where Perseus is. (Don't use the moon in the pictures -- the moon moves a lot from night to night). Probably the comet will be visible to the naked eye at least a few more days. Good luck!