The American Revolution did not solve all the problems in the newly formed United States. The "founding fathers" left the issue of slavery alone, not wanting to cause conflict and unable to resolve the issues themselves. They wrote that 80 years later the next generation could reassess it. Also, the issue of state power versus federal power was murky. Since the American Revolution aimed to break away from a monarchy and tyrranous federal government, the threat of having a strong federal government in the US wasn't unanimously accepted, creating the Federalist and Anti-Federalist parties. The Civil War addressed both these issues (as well as countless others) and, as we know, slavery was abolished in captured Confederate territories and eventually across the US with the 13th Ammendment. In the war Black Union Men were allowed to serve, as in the Massachusetts 54th infantry, but it would not be until the 1950's when civil rights for blacks would be instated and preserved. In a way the Civil War resolved the issue of slavery, but did not help former slaves attain all their rights. It did, however, bring about the 14th Ammendment which gave blacks the rights of citizenship which had been denied in 1857 in the case of Dred Scott v Sanford. Also, the Fifteenth Ammendment was passed which prohibited any state government from denying a citizen the right to vote based on "race, color, or previous condition of servitude."
State versus Federal Power was not resolved, but addressed through the Civil War as well. The fact that the government declared war in order to restore the Nation proved its power, as well as abolishing slavery and creating a stronger federal government. While we are still struggling with state versus federal power, we are a much more stable nation than we were before 1870.
Ultimately, the Civil War was a culmination of much tension that had built up in the US after the Revolutionary War. Slavery was finally dealt with and abolished, and the Federal Government made itself stronger in order to protect the nation and keep it united.