This is the Cigar Galaxy, also known as M82 or NGC 3034. It is found near the constellation Ursa Major. The Cigar Galaxy is particularly notable because of a strange object found within it. In 2010, we discovered an unknown object that is emitting a signal that seems to be rather unique, which is to say that we haven't found anything else like it in the universe (though they almost certainly are lurking out there somewhere). The object is putting out a large amount of radio waves, while producing very few x-rays. People have hypothesized that this is an unusual form of quasar, but so far we have failed to properly identify and categorize this mysterious object.
Other than the perplexing puzzle this galaxy presents, it's also known for being an extremely luminous object, with it being more than five times brighter than the Milky Way. It's so bright, in fact, that it outshines the central region of the Milky Way (the brightest part) by a factor of 100. Perhaps the catalyst for this huge starburst was a gravitational encounter, or a collision.
For more awesome pictures from the Hubble space telescope, check out this link.