In the American electoral system, a swing state is a state that is not strongly committed either way in a presidential election. In any given election year, probably around forty states are already solidly behind one candidate or the other, and would not switch under any normal circumstances. Thus, bringing about a majority in the electoral college means wooing voters in under a dozen states.
The inordinate amount of attention that candidates pay to swing states is one of the weaknesses of the electoral college. Candidates will blanket the airwaves of Ohio and Florida with commercials and make dozens of personal appearances, while ignoring some of the larger population centers in solid states such as New York, California and Texas. In certain situations, appealing to swing state voters may mean a candidate will make promises to champion that state's pet issue, such as the popular ethanol subsidy in Iowa. On the other hand, candidates do not totally ignore solid areas, because they will stop there for reasons of fund raising and down ballot elections. It is also true that swing states are often microcosms of American politics as a whole, so that a candidate who tries to appeal to the mix of urban, suburban and rural voters in states like Ohio and Florida is doing a good job of appealing to the electorate as a whole. Whatever the justifications for and against it are, swing states will be an important part of political campaigns unless the electoral college was abolished.
Since the current US political map was put into place around 1988 or 1992, with the coastal, urban areas being Democratic and the South and rural plains states being Republican, the swing states have been areas that combined aspects of the two of them. Thus, Ohio, Florida, Iowa and Missouri were swing states. The recent election has seemingly rearranged the political map, and it could be, based on how politics realign, that a totally different group of states will be considered swing states through the coming elections.