In the United States before the Civil War, when owning slaves was common, manumission was the act of setting a slave free.
When Hamilton sings about "revolutionary manumission abolitionists" in the musical Hamilton, he's being a tiny bit redundant. Manumission and abolition are both used to mean "freeing slaves" or "a release from slavery." More specifically though, manumission is the act of a slave owner setting slaves free, while emancipation (and abolition) involve government action. When slavery was legal in the U.S., most who opposed it believed in all three.