This is a coronal mass ejection (CME) - a massive release of electromagnetic energy and ionized (charged) particles, mostly electrons and protons. If the event occurs on the side of the Sun facing the Earth, electromagnetic energy from across the spectrum, long-wavelength radio waves to short-wavelength gamma rays, travel to Earth at the speed of light taking only 8.5 minutes or so to get here. The stream of charged particles takes a bit longer to reach the Earth traveling, on average, about 500 km/s although sometimes reaching speeds of 2000 km/s. Since the Sun is 150 million km away, it will take the charged particles anywhere from 1-4 days to arrive (depending on their speed).
These eruptions of energy on the Sun are associated with active regions - in other words sunspots. They're not well understood but are thought to occur when lines of magnetic force break and reconnect releasing stored energy. As much energy as a billion hydrogen bombs!
What are the consequences of this here on Earth?
Fortunately, here on Earth, we're shielded from much of the dangerous electromagnetic radiation (gamma rays and x-rays) and high-energy charged particles by the Earth's atmosphere and magnetic field. Future astronauts on the surface of the Moon, or traveling on a ship to Mars, could get radiation poisoning or even be killed by such events (astronauts aboard the International Space Station are in a low-Earth orbit and still somewhat shielded from such events).
OK, you're thinking, I'm not planning a trip to Mars anytime soon so what's the worry? The problem is that with a large enough CME, our atmosphere and magnetic field become a bit overwhelmed and there are effects here on Earth - some harmless and some more serious.
Our Earth has a magnetic field generated by the rotation of liquid iron in the outer core. This field normally deflects away the constant stream of charged particles from the Sun (the solar wind). This solar wind compresses the Earth's magnetic field on the side facing the Sun and stretches it out on the far side into a tail.
During a CME, so many charged particles (ions) interact with the magnetic field that some are able to leak down toward the Earth in the vicinity of the north and south magnetic poles. Some get trapped in a doughnut-shaped ring called the Van Allen radiation belt and others spiral into the upper atmosphere (called the ionosphere). These results in auroras.
More on auroras in a bit while we first take a short digression and talk about satellites and power grids...
Satellites are greatly affected by the charged particles released during a CME. Most satellites don't orbit in the vicinity of the Van Allen belt, but those that do need to have their electronic components radiation hardened to survive. Satellites in higher orbits are susceptible to damage from the high-energy particles from CMEs. High energy electrons can physically damage the electronics and solar cells of satellites and even scramble the data stored in computer chips.