The “Fifty-Four Forty or Fight” slogan can be traced back to the Oregon Border Dispute between Canada and the United States. The dispute emanated from the joint settlement of both Americans and British citizens in an undefined area along a previously established boundary. The situation led to both countries laying claim to the territory, with the countries involved trying to shift the boundary from what was earlier agreed. The agreed border was established along the 49th parallel, however, Americans wanted it shifted to the 54th 40 parallel, while the Canadians campaigned for the boundary to be shifted to the 42nd parallel. In the 1844 American election, James Polk campaigned and appealed to those supporting the expansionist agenda by suggesting that a violent encounter would ensue if the boundary was not shifted to the 54th 40 parallel. James Polk won the election, but he later abandoned the “54 40 or Fight” campaign, and the boundary was maintained along the 49th parallel.

This phrase was a slogan for people who wanted to expand the United States far to the north in the Oregon Territory.

According to a treaty that was signed in 1818, the US and Great Britain were to jointly occupy the Oregon Territory, from what is now the southern border of Oregon to the line at 54 degrees 40 minutes North latitude.

In the 1830s and 1840s, Americans started to want to expand.  The expansionists wanted the Oregon Territory to belong solely to the US.  The slogan you mention was used by the most extreme of the expansionists.  The meaning of the slogan was that the US should go to war with Britain unless Britain gave the US the entire Oregon Territory.

This issue ended with the boundary being set at the 49th parallel.