In American culture, the word is most commonly learned in American History classes in elementary school in conjunction with studying the Civil War. During the war, in 1862, President Abraham Lincoln signed an executive proclamation ending slavery in the Confederate States effective January 1, 1863. Though the proclamation was not immediately effective in Union States with slaves, this proclamation is widely viewed as the legal end of the institution of slavery in the United States.
Another form of emancipation was witnessed via the Haitian Revolution of 1804, when rebel slave armies defeated Napoleon's colonial forces and established independence through direct revolution. These independence struggles were termed emancipation struggles, or sometimes "self-determination" struggles. The national emancipation struggle that involved the largest population in the 20th century was India's struggle against British colonial occupation.
Manumission, a word that shares the root of the word "emancipation," means releasing someone from bondage. In this case, it's not emancipation by an outside political entity, such as the United States government; nor is it a self-generated emancipation struggle of a whole people. Manumission is the voluntary release of slaves by an individual owner. This was not an uncommon practice during several epochs and in several places -- for example, imperial Rome or the pre-Civil War United States.
The term "emancipation" can also refer to a gradual process of social change in which a subjected group gains more social power over time. The case of women in most modern nations is one in which there have been key watersheds, such as the right to vote, but also a part-by-part struggle against unequal treatment in various other arenas of social life. American women can vote, for example, but still struggle against economic inequality and dependency, as well as against male social power in the culture. This ongoing process is called emancipatory, without the finality yet of calling it emancipation.
Minors -- however defined by law in various countries and various states in the U.S. -- are not servants, but they are wards of specified adults, usually parents. Wards of minors can make decisions for them, such as where the minor lives or how to spend money. The legal age of majority is an automatic emancipation; but emancipation of a minor is a special case in which the governing court ends the ward's authority over the minor. Depending on the circumstance, the minor may be allowed to live on her own, or she may be placed under the supervision of a different ward.