All of these words come from the french revolution. In legislature, those who wanted to abandon the monarchy and adopt a constitution tended to sit on the left, while those who wanted to preserve, but perhaps reform the monarchy sat on the right. So those words came to be associated with each political tendency.
Liberal also comes from the french revolution. Liberal literally means free, so the liberals in France believed in basic freedoms and human rights that they were entitled to, similar to the American revolutionaries.
Conservative came later, during the Bourbon restoration, when the French monarchy was reestablished. The word was used to describe those who wanted a return to the ways of the past, particularly with respect to the monarchy. The word comes from “conserve”, in this case, conserving traditional values in the face of progressive change.

Now, modern politics has kind of warped and confused these terms, especially in America. Because today there are not many monarchies left, and most countries have a constitution and promise to protect human rights. So the world is predominantly boxed inside of liberal ideology. So much so that we fail to see it is an ideology at all, and take for granted many aspects of it, and fail to see outside of it. The people we call conservatives in the US, for the most part, are liberals too, they are just more conservative liberals.

I should also point out that the left is more than liberals during the French revolution as well. The French revolution was a kind of proto-communist movement. It was the inspiration for socialist and anarchist thinkers who came after. These ideas of socialism were not really well developed yet, and people didn’t really understand the problems with capitalism because capitalism hadn’t existed for long. Yet the French revolution was indisputably egalitarian in nature, because inequality in addition to lack of legal rights was a pressing concern for the French people who were starving while the nobles gorged themselves. This is where the phrase “eat the rich comes from”

tl;dr: The French revolution is the inspiration for our modern political framework. Left = Communism, Socialism, Liberalism. Generally progressive and egalitarian ideas.
Right = Monarchism, Reactionaries, the status quo. Generally those who oppose radical change or want to return to an idealized past.

Generally, right and left are a question of “power in the hands of the many” vs. “power in the hands of the few” or more specifically capitalism vs anti-capitalism. These have nothing to do with culture-war issues. Conservative and liberal are frankly just made-up US things and make less and less sense every passing year because Capital very effectively uses them to divide and sow dissent among the working class.

Left means collective property over resources (communism) which means everyone gets access according to their needs. Right means private property (capitalism) in which access to resources is defined by your wealth.

Conservative usually means authoritarian (another axis) in which some people can decide how others can live. Whether it’s via majority voting or dictated by a minority is irrelevant: anarchism (on the other side of that axis) accounts for protecting minorities as the key principle is that the lowest decision level (eg. the commune) is the one that counts.

“Liberal” can mean several things depending on the cultural/political context. Historically, it referred to a political school of freedom as opposed to centralized authority (an ancestor to anarchism). Nowadays, it can refer to the less-conservative positions (in the anglosaxon world, as opposed to conservative) or to capitalism (eg. in the latin world). From an anarchist perspective, “liberal” or “social-democrat” refers to very limited/narrow policy goals (reforms that do not attack the status quo of Nation States and private property) as opposed to revolutionary perspectives.

The political compass posted elsewhere in this thread is very informative, although more axis should be considered if you want a profound reviews of political positions. It’s interesting to note that in many cases, people whose ideas would fit in the lower-left quadrant (anarcho-communism) end up voting for politicians who overwhelmingly represent the top-right and bottom-right quadrants.

I like to think of right vs left on the capitalist vs. anti-capitalist axis.

So, a socialist is further to the “left” than Joe Biden, but Joe Biden is slightly left of Ted Cruz (on this definition).

There is an occasional meme in the culture to jettison these terms because they’re vague. I still think the terms are useful, because it recognizes that our current situation is historical. Every current political phenomenon has historical antecedents, often centuries-old.

Of course, we also need to be careful not to split hairs, and use big obscure words, like some of us on “the Left” like to do. :) Clarifying what we’re talking about is always a useful exercise.

So, I still think “right” and “left” are useful terms.

My overly simplistic explanation:

The Right: Want to keep the status quo. Change is unnecessary. Tradition is paramount.

The Left: Wants to improve things. They see an injustice and want to correct it.

They are whatever you want them to be. The terms are relative and lack nuance.

A conservative will call a liberal a leftist, and a liberal will assert that a conservative is “on the right”. People will say that a fascist is “on the right” and also a libertarian is “on the right”. People will say they are “to the left on economic issues, but to the right on social issues”. All of these takes lack real nuance because they tell you basically nothing about the person you are speaking to, unless you already know what they mean by their version of left vs. right.

The 2d polcomp is a meme anyway and nobody should use it for serious discussion.

This is in now way an official definition, but to me, Right and Left can be explained by adding two prefixes to part of a word:

clusive

The Left is all about being INclusive. The Right is all about EXclusive, in all senses of the word.

Alongside Left and RIght, there’s also Authoritarian, and Libertarian - how much power the state has, versus how much freedom an individual has. See politicalcompass.org/ They also have a questionnaire which if you can answer honestly, will tell you where you fit in the political spectrum.