If you emancipate someone, you set them free from something. At the end of the Civil War, slaves were emancipated and became free men and women.
If you break down emancipate, you have e- "out," -man- from the Latin manus "hand," and -cip- from the Latin verb "to take." Put it together, and you have "to be taken out of someone's hands" — a good definition of freedom. The American Revolution was about colonists emancipating themselves from British rule. As a legal term, if a child is emancipated, he or she is declared independent from parental control.