Hi!
A solar storm is the ejection of solar material out from the Sun. If the solar material moves in the direction of the Earth, it can indeed affect us! Generally speaking we are protected by the Earth's magnetic field, but we can feel the solar storm's effects in several ways -- highly energetic particles come along with and in advance of the solar material and get in through the Earth's magnetic fields at the poles -- causing the aurorae, e.g. the Northern lights. Ground currents can also be induced at polar latitudes, and this can cause problems with electrical power grids; in 1986 several of Canada's NE provinces were blacked out because of this. The actual solar material can buffet and otherwise interact with the Earth's magnetic fields, causing damage to satellites.
cheers,
Sarah