If I recall correctly, Lincoln was in favor of abolition, while Douglas was in favor of leaving it up to the states.
Lincoln was not (publicly) in favor of abolition. He was in favor of banning it in DC and the territories, though. Douglas was in favor of allowing the residents of a territory to ban it, which amounted, in practice, to the same thing. As everybody knew.
More important was that Lincoln's Republican supporters were adamantly anti-slavery while the Northern Democrats (though not necessarily Douglas specifically) were only half-heartedly anti-slavery.
Can someone explain this?
You don't know the meaning of the word half-heartedly? Because in that case, it means that one is not fully dedicated, does not have one's whole heart in it, so to speak. I don't see what else could be unclear.