I think that the main impact of the abolitionist movement is that it helped to end slavery in the United States. Of course, it was not mainly the abolitionists who did this -- it was the Civil War. But the abolitionists helped to bring about the Civil War and helped in some ways to make the war be about slavery.
If it had not been for the abolitionists, there would have been less animosity between the North and the South. The two sides would still have had major differences, but they would have been somewhat less emotional. The abolitionists tried to demonize (with reason, to be sure) the slave system and slave owners. This made the conflict more personal and it made the South more afraid of and suspicious of the motives of the North.
Because the abolitionists made slavery such an emotional issue, they made compromise less likely and made war more likely. Since this war freed the slaves, you can say the abolitionists helped to free the slaves.
For thirty years prior to the Civil War, Abolitionists worked to fight slavery. The impact they made on United States citizens was one of raising awareness and eliciting emotion against the use of slaves. For decades, slavery had been a huge part of the U.S. economy but not everyone agreed that it was morally acceptable. People in both the North and the South disagreed with the practice but did not argue or speak up because of the economic impact.
The Abolitionists capitalized on the segment of society that was unsure of slavery's moral standing, especially in a country founded on freedom and equal rights. Over the first two decades of the 1800s, they raised awareness for their cause using increasingly defiant measures that called to end slavery. By 1850, there was a large faction of U.S. citizens who felt slavery was wrong. The Abolitionists stirred emotion and a call to action within those citizens, calling for an immediate end to slavery. Emotions ran high during the decade leading up to the start of the Civil War.
Without the Abolitionists, citizens may have taken much longer to reach a point of Civil War as a means to end slavery. The emotional responses that Abolitionists were able to elicit brought about the acts that led to the first battles of the Civil War.