Geomagnetic storms are the result of solar events that subsequently impact earth's ionosphere. They are graded from G1 (the mildest) to G5 (most severe) and the grade can be derived from the K-index (one of the many solar related values published NOAA). A Kp index value of 5 equates to a G1 and a value of 9 equates to a G5.
The predicted G3 storm for tomorrow is classified as a Strong storm by NOAA's standards and is the result of a Coronal Mass Ejection (CME). CMEs are large clouds of plasma (ionized gases) that have been ejected from the surface of the sun. They are directional, and occur with some regularity, but are only a problem if the mass of particles heads our way.
When they do head our way and impact the ionosphere, they cause a number of changes. Due to increased ionization of the lower levels of the ionosphere, signals between 2MHz and 30MHz will experienced increased absorption; if the storm is bad enough, that's 100% absorption.
Areas in the auroral zones are hardest it. During these storms they can experience rapid
and deep signal fading due to the ionospheric irregularities that scatter the radio signal to the point that communication is impossible.
On frequencies above 30MHz, unexpected reflections of the radio waves by the ionosphere may cause radio interference. Ionospheric irregularities may produce fluctuating signals (a phenomenon known as scintillation) and may distort the paths of radio waves. If strong enough, this can adversely impact phase-sensitive systems on frequencies above 1 GHz (e.g., the Global Positioning System; talk about potential mayhem).
Other effects include Auroral absorption, multipathing, and non-great-circle propagation. One possible happy effect (for those living in the mid and upper latitudes) is that the auroral zone moves equatorward giving folks who are not normally able to experience the aurora a chance to see them. And since propagation will be garbage, you may as well go outside and look.
Other effects that could be important: some minor impact on the power grid by inducing some voltage fluctuations. Spacecraft may observe some surface charging on satellite components, drag may increase on low-Earth-orbit satellites, and corrections may be needed for orientation problems.