An individual is unemployed if she does not have a job, but she is actively searching for one. The unemployment rate is, therefore, the percentage of the labor force (those who either have a job, or are actively searching for one) who do not have a job; it is determined by means of a survey.
Why does unemployment matter? Consider the textbook model of the labor market. The labor demand schedule (D) relates the quantity of work would-be employers want to buy to the level of wages. The labor supply schedule (S) relates the quantity of work would-be employees want to sell to the level of wages. In equilibrium, the level of wages (P) is determined by the intersection of the labor demand and labor supply schedules. Because employers want to buy more work when the level of wages is lower, the labor demand schedule slopes down. Because employees want to sell more work when the level of wages is higher, the labor supply schedule slopes up:
Suppose that, for whatever reason, the level of wages is too high (in the diagram, higher than P). The quantity of work employees want to sell (the labor force) exceeds the quantity of work employers want to buy (employment). Unemployment, in this model, is the excess supply of labor due to wages being too high. Lower wages increase employer surplus more than they decrease employee surplus--that is, lower wages (provided compensating transfers) can make everyone in the labor market better off. Unemployment thus signals labor market inefficiency.
For the sake of efficiency, then, we want zero unemployment, right? Not quite. In order for dynamic economies to efficiently allocate labor, it is necessary for workers to change jobs from time to time. At every point in time, therefore, some "natural" fraction of the labor force is in between jobs, resulting in a non-zero unemployment rate. Moreover, because the unemployment rate is determined by survey, some individuals outside of the labor force may pretend to be actively searching for a job (for various reasons), further elevating the unemployment rate. The "natural rate of unemployment" is, consequently, thought to be significantly greater than zero.
What causes high unemployment? Demand-side stories cite contracting labor demand in the face of sticky wages. Supply-side stories cite contracting labor supply masquerading as contracting labor demand. Demand deficiencies cause unemployment rates in excess of the natural rate, while supply deficiencies cause the natural rate itself to rise. The mark of demand deficiency is slowing or static wage growth, while the mark of supply deficiency is rising wages.
It is important to correctly identify the cause. To see this, note that if the problem is demand deficiency, a fix for supply deficiency (encouraging workers to seek employment) raises, not lowers, the unemployment rate. If the problem is supply deficiency, a fix for demand deficiency (encouraging firms to hire more workers) does little or nothing to the unemployment rate, but creates other problems (e.g., excess inflation).
So, why is the unemployment rate in the US so high?
Looks to me like slowing or static wage growth since the onset of the recent crisis. Looks to me, therefore, like demand deficiency is the problem. The prescription for lower unemployment rates, then, is more work, not more workers. And the prescription for more work, recall, is greater aggregate demand for US economic output.