So, Philae made it. For the first time, humans have landed a spaceship on a comet. It did not go entirely smoothly - the lander is in good shape but the harpoons designed to keep it in place have not fired properly. They're hopefully fixing that right now.
Why go to comets?
Comets are an interesting phenomenon. Most of them spend their existence in the Oort Cloud, the furthest extremes of the solar system. Only a few get nudged out of it to dive towards the sun and become the tailed beasts we are familiar with. (I use the word beast with thought - Medieval people thought comets were living things, possibly dragons). In the past, comets were considered bad omens. Now, we consider them to be fun natural light shows.
They're more than that. Comets are giant "dirty snowballs". They contain water and other volatiles such as methane and carbon dioxide. Capturing comets may prove to be a way to provide these substances to space missions (it's expensive to lift anything out of a gravity well and water is heavy).
Comets also contain organic chemicals - and our own oort cloud extends far enough out to overlap with that of Alpha Centauri, possibly meaning comets are traded between solar systems, at least when they're close together. A close study of comets may provide evidence for or against seeding theory - not the intelligent alien version (which I do not believe in) but the theory that the basic stuff of life may have come here from somewhere else. Or, more likely, is constantly being moved around. The composition of comets might also tell us something about other forms life might take and how common it might be in the universe.
And comets, unlike asteroids, don't survive if they hit the Earth - at one point, some scientists believed that the Tunguska event was caused by a comet, but it's now been pretty much proven it was a rocky asteroid, probably blowing up in the upper atmosphere.
Plenty of reasons to do this and I applaud the ESA team on their efforts and success.