Reconstruction is the name given to the period of U.S. history following the American Civil War. The literal meaning of the era is the reconstruction of the southern states which made up the Confederate States of America from the devastation wrought by the war.
Reconstruction also has figurative meanings. The former states that made up the Confederacy were not admitted back into the union immediately. They were occupied by forces of the United States (northern) army and under martial law. Many radical Republicans, known as carpetbaggers, were "shipped" from up-north to the southern states to re-form their governments. Many southerners actually sympathized with the aims of Reconstruction, and worked with the military-backed governments. Their compatriots dubbed them "scalawags."
Since the early 1900s, Reconstruction has had a fairly bad reputation in the United States. Many history textbooks talk about the "radical Republicans" and their desire to "destroy" the power of the South. What's usually left out is that this "destruction" was to take the form of giving education and political rights to southern African-Americans in recompense for the horrors they'd endured under slavery. It was at this time that the US had its first African-American Congressmen, and even an African-American Senator.
Reconstruction came to an end mostly because the southern whites would not allow any political rights for southern African-Americans, and waged a vicious insurgency against it. It was during this time that the Ku Klux Klan was created. In the end, Reconstruction ended as part of a bargain in which southern states that had disputed votes for electors to the electoral college would allow the Republican candidate, Rutherford B. Hayes to win their votes in exchange for Hayes' withdrawal of the military governments. As soon as it ended, Jim Crow and segregation started.