A state whose voting outcome in a presidential election is relatively sensitive or responsive to changes in political conditions, such as a change in the national economic mood.
Nate Silver: “Elastic states are those which have a lot of swing voters — that is, voters who could plausibly vote for either party’s candidate. A swing voter is very likely to be an independent voter, since registered Republicans and registered Democrats vote with their party at least 90 percent of the time in most presidential elections. The swing voter is also likely to be devoid of other characteristics that are very strong predictors of voting behavior.”
An inelastic state, by contrast, is one which is relatively insensitive to these changes.