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.