Hello Megan,
Solar storms are made up of two main phenomena: soalr flares and coronal mass ejections. Solar Flares are sudden and short-lived (about 1 hour) enhancements acorss the electromagnetic spectrum. The solar atmosphere gets heated up to 30 or 40 million degrees during a flare and electrons and protons can be accelerated to speeds very close to the speed of light. Coronal Mass Ejections (or CMEs) are expulsions of material from the Sun caused by the rapid release of energy in the solar atmosphere. About 10^15 g of plasma is ejected from the Sun at speeds exceeding 1500 km/s (that's athe mass of mount everest traveling at over 1 million miles per hour!). Thesefast CMEs run into the slower solar wind creatin a shock, a bit liek a jet creating a sonic boom. This shock accelerates electrons, protons and ions to very high energies and these particles stream towards the Earth and interact with our magnetic field and atmosphere. For the largest storms, satellite electronics can be short-circuited, currents can be induced in ground-based electrical systems and the radiation dose for high altitude air crews and astronauts can reach dangerous levels.
Cheers - David