The border at Point Roberts is born of the same stock that created the border between the US and Canada at the Northwest Angle in Minnesota, human error. It is also an example of realities on the ground getting in the way of plans made far away without local knowledge. The result is this small piece of the State of Washington that can only be reached by car by first driving into Canada and then driving back down across the border here. It is considered to be part of the “mainland” continental US even though it is physically connected to it.
Point Roberts is also connected to what has to be one of the more esoteric presidential campaign slogans. President James K Polk was elected in part by running under the slogan, “Fifty-Four Forty or Fight”, a reference to the border between US and British territory at 54°40′ North Latitude. What is now Oregon and Washington was then disputed territory between Mexican-held California, Russian America and expanding British and US interests to the East. Most of what is now the border between the US and Canada follows the 49th Parallel. Extending this west to the Pacific however would mean the border would go straight across Vancouver Island and separate the British stronghold of Victoria from the rest of British-held territory. The eventual compromise was the bend in the border we see today that gives all of Vancouver Island to Canada. It all makes sense when you zoom out a little except that the same problem that existed with Vancouver Island happens at Point Roberts. Unfortunately this detail was not discovered until much later and the border stuck.
Sources: Wikipedia