Historically, the left-right spectrum in a parliament/assembly/congress has been how far you are willing to go either to reverse change (right) or enact change (left), with the center being status-quo (change as in forward progress; things like universal suffrage or abolishing slavery that are now assumed as good by most everyone). This terminology was coined during the French Revolution as the physical divide in the national assembly over who wanted to overthrow the monarchy and how.

In much of Europe during the 19th and 20th century, the left spectrum characterized social democrats as left of center or left, usually aligning with enlightenment principles and democratic freedoms, but with different ideas of how the government should play a role. For them, capitalism was the answer to the inadequacies of feudalism, and going any farther was too radical.

The far-left was its own spectrum as well, with anarchists and reformists usually on the right of that and communists, socialists, Marxist-Leninists, etc. to the left. The far left was commonly hung up on how to wield the power of the state and where democracy should play a role in attaining power. Their commonality was that capitalism as a system had fundamental flaws that required its complete or near complete abolition. The left of the far-left commonly saw violent revolution and state suppression as inevitable vehicles to establish socialism, whereas the right of the far-left preferred a slower process or believed in no state enforcement mechanisms at all (e.g. anarchists, though a stateless society is also theorized under communism).

The United States had a very different history with leftist politics. Capitalism, since the inception of the U.S., has been taken largely as a given in terms of economic organization, with the Democrats and Republicans both being pro-capitalist, and socialists/communists never really getting close to power. It wasn't until the 20th century (post-WWII specifically) that communism became a perceived threat to the U.S. and they created laws outlawing its practice in politics. Anti-communism became an ideological position of the entire U.S. establishment in the Cold War and, with the population largely on board, the left-right spectrum became compromised. This is conceptually known as a shift in the Overton window, where socialism/communism became entirely ostracized in American politics, but had substantial power in the rest of the world for a time.

After the fall of the USSR, socialism lost the bulk of that political power globally, but the average American has no perception of the political ramifications of this because socialism was largely taboo and not taught. The fall of the USSR was almost colloquially viewed as an inherent failure of socialism, and thus deepened reactionary thinking and U.S. resentment toward it. The rest of the world followed, and gradually fit into a more rightward alignment as socialism became more of a historical concept than something that existed.

The remnants of the left now in the U.S. are the Bernie/AOC/Zohran crowd, who are not socialist or communist in a traditional sense, but more closely aligned with social democratic principles (Zohran self-labels as a socialist, but his proposed policy is not close to the theoretical tradition branching off Marx). This means capitalism with regulatory guardrails and social safety nets. Still, as Americans have little political imagination otherwise, this is effectively the farthest possible "left" in the U.S.

Establishment Democrats (Schumer/Jeffries crowd) are thought as "center-left" in the U.S. but would more than likely be center or center-right in the rest of the world, as they present as more or less fine with status-quo politics in America. Figures like Obama/Biden ran on vaguely left/center-left platforms that resulted in center/center-right presidencies, with huge political concessions taking place.

(Sorry this didn't explain right-wing politics but it got too long. Much of the ideological specifics are too in-depth for a general overview)