[jump to explanation]
What does the "Kp index" mean? What does it have to do with the phenomenon of auroras (aurora borealis occur in the northern hemisphere, and the aurora australis occur in the southern hemisphere)? Well, the auroras are caused by excited particles in the atmosphere returning to their normal state and thus releasing protons. The particles in the geomagnetic field of the Earth are excited when they are struck by radiation from the sun during geomagnetic storms. As the field adjusts to this energy, it releases magnetic energy which streams along the geomagnetic field lines. It's this energy that when it ends up in the neutral part of the atmosphere, and is released, causes the auroras.
This geomagnetic disturbance can then be measured by machines called magnetometers. The data is then packaged into indices for 3 hour periods, called K-indices. The K-index ranges from 0 to 9 (where 0 is the lowest) and represent the measurements at a specific observatory. Since this phenomenon is not what is called "spatially homologous" (meaning its not evenly spread out, but rather concentrates at specific pockets) it is not enough to know what the K-index at another observatory is (see the pictures of auroras to see roughly what this means).
Also, as the disturbances increase in intensity the latitudes at which it can be observed also expand, meaning that the stronger the disturbance, the more south (in the case of aurora borealis) it can be observed. Since the locations at which the auroras can be observed span an oval-shaped region, also called the auroral oval, we can see on the auroral oval plot above whether we are in a latitude in which they can be observed.
The Kp-index is basically a calculated average index of the K-indices of several of these observatories. The Kp-latitude map above shows how high the Kp index has to be for auroras to be visible at that latitude. So, along with the Kp index plot (estimated planetary K-index), and a good notion of where on the map you are, you can find whether you can see auroras where you are right now.
And here's an excellent video by NASA's Solar Dynamics Observatory, which also explains sun spots and other solar-related phenomena.
NASA SDO - Aurora; What Causes Them?
Aurora are colorful lights in the night time sky primarily appearing in Earth's polar regions. But what causes them? The culprit behind aurora is our own Sun and the solar plasma that is ejected during a magnetic event like a flare or a coronal mass ejection. This plasma travels outward along with the solar wind and when it encounters Earth's magnetic field, it travels down the field lines that connect at the poles. Atoms in the plasma interacts with atoms in Earth's upper atmosphere.
+ view video
Here are some books recommended by the guys at SpaceWeather.com (an excellent site, by the way):
An old, but classic text is The Polar Aurora, Oxford University Press, 1955, by Störmer.A more modern text is The Physics of Space Plasmas, 1991, by George Parks.