The Era of Good Feelings came about almost directly as a result of the War of 1812 and the subsequent destruction of the Federalist Party, which was one of the two major parties in what is called the "First Party System."

The first party system is more or less a way to describe the political poles around which American politicians and elites collected themselves after the ratification of the constitution. The poles had always been there in American colonial politics, and were expressions of a broader political theory called Classical Republicanism. Most of the salient elements of the constitution, and even of the articles of confederation, were based on the idea of classical republicanism: promotion of the common good, the rights of man, the ideas around private property and civic virtue, a representative government, etc.

Ratifying the constitution distilled these poles into two distinct and opposing groups, roughly around whether or not they supported the constitution. Those in favor called themselves "federalists" who believed that the nascent state would function better with a stronger federal government. Those opposed called themselves "anti-federalists" and believed that the state would function better with a far more distributed government network with power coalescing at the state level.

Before we go on any further, I want to say that there is a frustrating trend in current political historiography - even by otherwise excellent writers - to align these groups with the modern political paradigm, and say without irony that "anti-federalists are the forerunners to the republican party" or vice versa, and to do that through more or less every political era. In doing so, these writers remove all attempts at exploring what these beliefs meant in their own context and obfuscate the important conceptual and philosophical differences between now and then. It's badhistory. So, I won't be trying to make thin connections between either side and the current political climate.

Anyway. The federalists and anti-federalists had their skirmishes in the runup to ratification, and after the smoke cleared and the United States had a newly powerful federal government to contend with, sides once again coalesced around the hot issues of the day, but with the ratification, the anti-federalists needed to re-brand. It took a few years, but eventually they started calling themselves the "Democrat-Republicans" (and here we arrive at another pebble in the shoe of trying to neatly fit late 18th century politics into a modern framework).

Democracy and Republic both sounded great to an 18th century audience, right? Sort of. "Democracy" was thought of by some thinkers as "mob rule" and ideas like universal (white male) suffrage were considered radical populism to the point of demagoguery, just stir up the mob and get your way. Especially considering that the mob already had a means to vote, which was by publicly voicing their concerns through their representatives, or, failing that, politics out of doors: rioting, property destruction, and other forms of political violence. This was an expected part of politics at the time, but it was never uncontroversial.

Democratic-Republicans, though, rhetorically took the side of the "little guy" and championed their rights so long as those issues also helped to empower or entrench the power of southern plantation owners, who made up the bulk of the democratic republicans. In their ranks stood men like James Madison, James Monroe, and Thomas Jefferson, the latter of whom became the emblematic leader of the party.

Federalists, on the other hand, were more concerned about state building. Obnoxious and disliked men like John Adams and Alexander Hamilton felt that there could really be no success as a country without the respect of other states, and especially that of Great Britain, and they felt that flexing federal power was one way they could do that. They envisioned taxes paying for ambitious road systems to link north and south, a robust financial system to get into the international credit scene, a small federal army and navy with the ability to project American power, and an overhaul of the militia system to make territorial defense a priority, even if this meant curtailing the power of southern plantation owners and even powerful, fabulously wealthy men in their own ranks.

This is all a very superficial rundown of the political poles, by the way, there is far too much nuance to really express here. Basically, the federalists believed that most political problems could or should be solved by action of the federal government, and the Democratic-Republicans felt that power should be collected by states themselves. All of these men would easily benefit personally, financially or otherwise, by the disposition of American power. No one was an objective actor here, even if they all tried to say they were.

This system lasts through the crises of the 1780s and 90s and into the first decades of the 19th century. George Washington, while never officially a member of either party was in temperament and action a thoroughgoing Federalist, and his successor Adams was more or less the Federalist figurehead afterward, and his successor was Alexander Hamilton, whose more fiery brand of militaristic, financial federalism became the face of the party after Thomas Jefferson's election in 1800.

Jefferson pens democratic rhetoric with one hand while using the tools left over from the federalist years with the other, and to skim over the first tumultuous decade of the 19th century, used the federal power in essentially the same way the federalists had, going so far as to, during the crisis with Great Britain in the lead-up to the War of 1812, outlaw international trade and to increase the size of the US army and navy to nearly unprecedented levels.

When the war eventually starts, there are two clear sides in American politics: the still robust minority party in the Federalists and the Democratic-Republicans, whose star was still rising. Federalists opposed it on moral, financial and political grounds, and the Democratic Republicans felt that it was a necessary recourse for the injuries suffered at the hands of Great Britain. You can read more about it from an earlier answer of mine.

To make a complicated story short, the US did not do well in the first stages of the war but continued to fight, nearly bankrupting the country and coming close to being refused loans to continue paying for it, the Hartford Convention of Federalists old and new threatened but pulled short of a possible northern secession, and ultimately, the war ended in a way that vindicated Jefferson's policies, the near failures all collectively heaped on the bad-faith actors of the Federalist party, who were accused of sedition in all but name. Against the rising tide of patriotic fervor that swept the United States after their supposed victory, Federalists looked like traitors, ineffective and old fashioned, and essentially crumbled as an organized party of minority.

This meant that in order to maintain their positions in politics, Federalists had to disavow some of their Federalism and embrace Jeffersonian populism, at least in its more visible aspects. This is where the idea of "Good Feelings" comes from: everyone was on the same team, and that team was AMERICA.

None of which is to say that there wasn't a great deal of political turmoil or disagreements at the time, just that because the Federalist party was organized in a bunch of smaller, more single-issue focused parties, they couldn't muster any organized resistance to the party of Majority.

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One of the better books on the first party system and its republican undertones is Lawrence Cress's Citizens in Arms which is about the militia, but covers a good deal of philosophical ground.

Another that covers some of the political spats before and following ratification is Richard Kohn, Eagle and Sword

And for more specific info about "politics out of doors" and ways in which the disenfranchised were forced to express themselves and how that came to an end, Paul Giljie's article "The Baltimore Riots"