To what did the Democratic slogan "Fifty-Four Forty or Fight" refer?

This slogan referred to a line of latitude.  “Fifty four-forty” means fifty four degrees, forty minutes North latitude.  This was the line of latitude that some Democrats wanted the United States to have as its northern boundary in the Pacific Northwest.  The slogan calls for the US to go to war if it is not given this boundary.

In 1818, the United States and the United Kingdom signed a treaty in which they agreed to jointly occupy what was called the Oregon Territory. This territory stretched from what is now the southern border of the state of Oregon up to the 54-40 line (the southern limit of Russian Alaska at that time).  By the 1840s, many Americans wanted to expand their territory.  This was, after all, the time of Manifest Destiny.  The most aggressive Americans wanted to expand both in the south and in the north.  They supported war with Mexico to gain more land in the south and they demanded that Britain give the US all of the Oregon Territory.

The slogan “fifty four-forty or fight” refers to this demand.  The slogan meant that the US should go to war with Britain if the British did not give the US all of the Oregon Territory.  The US did not end up going to war with Britain and Britain did not give the US all of the Oregon Territory.  Instead, the US and Britain divided the territory.  They set the border at the 49th parallel, where it now stands.