1877 is regarded as the end of Reconstruction. Ostensibly, this meant that the issues leading to Civil War between the Northern and Southern sections of the country had been adequately resolved and the former Confederacy was successfully re-integrated into the Union. The end of Reconstruction stems from a compromise between the Democrat and Republican parties which concluded the particularly fractious Election of 1876. Samuel Tilden, the Democratic candidate, had won the popular vote by the most narrow of margins over his Republican counterpart, Rutherford B. Hayes. The Republican party had hitherto enjoyed political supremacy over the Democrats in the wake of the American Civil War but was now in a precarious position owing to the well-publicized corruption which plagued the outgoing Grant administration. To maintain its hold, the Republicans agreed to pull Federal troops from the former Confederate states in return for Tilden and the Democrats conceding the election. That, I suppose, is the "narrative" significance of 1877.

Considering the issues which necessitated Reconstruction following Civil War, slavery stands out as the most obvious and consequential. The "peculiar institution" of slavery was the foremost social and political question facing the United States and with its abolition with the 13th, 14th, and 15th Amendments it ceased to be such an all-encompassing consideration. New social and political challenges would have to fill the void and be faced by a country (supposedly) fundamentally changed by the results of Civil War and Reconstruction. The legacy of a slave-holding society in the South was of course still very strongly felt for a very long time and Reconstruction, by most interpretations, failed to rectify the inequities wrought by the institution of slavery in the former Confederacy.

Because it's convenient :/

Historians could (and do) argue about the significance of the Compromise of 1877 and its related context, and debate whether it's a more significant watershed than, say, 1865 (not-so-coincidentally, some universities split their US History surveys at 1865 instead of 1877), but the answer is far simpler: US history is too long for one semester, and the line has to be drawn somewhere. The US Civil War and Reconstruction are are incredibly pivotal and important moments (though how important and how pivotal varies) that happen to take place reasonably close to the "middle" of the timeline if we start in 1776***. It's the act of triage that makes the most "sense."

It's also very problematic because it creates a sense of separation between the two periods that is artificial and arbitrary. Many first half surveys (to 1865/1877) fail to adequately convey the momentum present in the Civil War era that heavily steered industrialization, the Gilded Age, etc. Many second half (1865/77 to present) surveys tend to ignore those same pre-war vectors. The Civil War then becomes a spike which treats both sides of US history as discrete and separate, and it's not just the surveys. American history booklists are plagued with monographs which start or end their investigations in 1865 or 1877, and ignore the trends which bridge both sides of the war.

There's also the issue of coverage. Whatever the title of the course says, Reconstruction itself is often glossed over. Too often, it's either crammed into the end of a tiring semester where the professor fell behind, or else glossed over as a prologue before getting to late-19th century politics and economics. Instructors on both sides try to rush through it assuming the other side will get it, which is a shame considering how vital Reconstruction is to understanding subsequent US history.

If it were feasible, I'd split the US survey into three (Colonial, 1776-1900 or whatever, and 20th century) and try to pick another arbitrary division that poses fewer problems. However, the two-semester setup is just too convenient for most universities to consider altering it.

In other words, the answer to your question is more administrative than historical, and it's a damn shame.

*** Writing that created a great disturbance in the Force, as colonialists everywhere cried out, and were saddened...