How did the abolitionist movement promote the idea of freedom as universal, and thus alter the national definition of liberty?
The abolition movement promoted the idea that freedom was universal; that it applied to African Americans just as much as it applied to white people. It also helped to bring about the idea that women had rights equal to those of men. This changed (or at least started to change) the American definition of liberty.
Before the abolitionist movement, the American definition of liberty was somewhat limited. It was believed that true liberty should only be open to white men. In fact, there had been the idea, not long before the abolitionist movement arose, that only white men with certain amounts of property should enjoy complete liberty. The abolitionist movement helped to do away with this idea.
With the abolitionist movement came the idea that the promises of the Declaration of Independence should apply to all people. This was the first time that a serious push arose to expand the meaning of freedom to encompass anyone other than white males. (Of course, this push did not succeed in the short term as slavery continued and then discrimination against blacks continued long after slavery was abolished.)
In this way, the abolitionist movement helped to start a major change in the national definition of liberty,