The Confederate States of America (CSA) needed international support in the Civil War because the Union had a much larger population and a much more industrialized economy. Specifically, they looked to Great Britain and France for help.
France had previously helped the Americans during the Revolutionary War, and many British citizens still harbored resentment toward the United States. The CSA recognized that Britain and France would probably not declare war on the United States, but they hoped that they would at least give them support, recognize their status as an independent nation, and mediate peace with the Union.
However, this bid for international support failed because these European nations did not want to be drawn into a war with the United States. President Lincoln's administration took a hard line against Great Britain and France, informing them that the Union would consider any European intervention as an act of war against the United States. Moreover, as the war progressed, the Union began to view the conflict as an assault on the institution of slavery. Britain was fiercely abolitionist, so they did not want to be responsible for preserving slavery in America.