The fragments of 73P/Schwassmann-Wachmann, a comet, will be visible with the naked eye in the nighttime skies over the next few weeks.

No, it will not hit the Earth and destroy life as we know it.

If you can wade through the geekdom, this web page may help you determine when and where to look (scroll down past the news section).  Alternatively, the charts here may be easier to understand.  Remember, because the comet is breaking up, there are several "components" (or fragments) which have different tracks and viewing times.

The picture below is a recent shot of Fragment B: