Galaxies are vast islands in space, stars, gas, and dust held together by their mutual gravity. Many sport grand shapes: elliptical, spirals, barred spirals, and so on. Some are just a mess, irregular in shape. Others are called peculiar: they appear to have some overall shape, but it's weird, distorted, like something bad happened.
For the Antennae Galaxies, something very bad indeed happened: they collided. Two massive spiral galaxies slammed into each other, their mutual gravity ripping out long streamers of gas and stars from each other. In general, the stars will pass by each other without a physical collision. Stars are very small compared to the space between them, and it would be like two dust motes inside an otherwise empty football stadium colliding with each other by chance.
But the gas clouds are big, and they do in fact collide. At the centers of the galaxies these clouds ram each other, collapse, and form stars at a furious rate. A new Hubble image of the Antennae shows this very well. The cores of the galaxies are all you can see here. The pearly glow is from old stars, the dark lanes are dust, and the cherry red is from the vast amounts of gas being lit up by newly formed stars.
If you were on a planet orbiting a star anywhere near the center of that mess, you'd be in big trouble. All that star formation means lots of massive stars, which in turn means a flood of ultraviolet radiation coming out of the core. But far worse, those stars won't last long: they explode, go supernova, and send out all sorts of nasty particles and radiation. If you're far enough away it's not a big problem, but there are a lot of stars ready to blow down there. I can't imagine what it would be like to see dozens, hundreds of supernova all going off in an astronomically short time... and I hope I never do.
The galaxies started colliding about 500 million years ago, and it will be a long, long time before this dance plays out. In the end, there can only be one: the two will merge, forming a larger elliptical galaxy. We see evidence of this everywhere -- ellipticals with multiple cores (indicating they formed from mergers), ellipticals with younger stars than expected, and of course many other galaxies caught in flagrante delicto as they collide. Our own Milky Way will one day collide with the monster Andromeda Galaxy... but not for over a billion years. So you can breathe easy for now.