Right, what do they mean by white supremacy? (By “they” I mean anyone who uses that term).

Generally on the internet it's used as a blanket insult largely devoid of meaning beyond "someone who disagrees with me". Similar to how a child will call everything they don't like unfair. Which is a disturbing trend as it makes it impossible to identify the actual racists as they can simply hide behind the storm of people claiming math is white supremacy or some such nonsense.

When the media uses white supremacy it's largely used as a kind of veiled political threat, it's mostly a distraction as a scapegoat for politicians failure to govern well and a deflection tactic to put people on the defensive when they question the politicians about their failed policies.

Actual white supremacy is when people believe white people are superior to all else and seek to implement a society where skin color and racial background are the defining aspects of one's life. The popular culture likes to focus on the KKK, Nazis and other historical groups that, to be fair, still exist in some form, however they are nowhere near as influential as they once were. Most modern white supremacy takes the form as the "soft bigotry of low expectations" largely from the left in the form of policies that assume that minorities are inferior and therefore entitled to extra benefits, affirmative action, lower standards, etc. Most highly educated people aren't quite so obvious about it and can understand some academic and macro-economic arguments that don't come from a place of believing in the innate superiority of white people, which is where most of these ideas are first discussed. However the internet allows for the lowest common denominator of discourse to take root and society and bureaucracies are filled with many low level drones who will simply repeat what they are told like NPC in a video game rather than trying to understand and dissect these ideas.

Most of the racial issues in the west aren't truly racial and are instead largely driven by economic class issues as well as cultural and religious issues. You'd be hard pressed to find anyone who is a true racist in the west in the sense where they equate skin color with value, but that was always the most easily digested and childish view of racism to begin with. Even in the past such issues were far more complex than we want to view them now.

It's also worth pointing out that pretty much all taxonomic classifications of race have little to no scientific value and that our views of where one race ends and another begins are basically driven by those same cultural and economic viewpoints of our contemporary society, as were those views in past socieites. We can choose basically any inherited feature as a racial characteristic. You get plopped back in Medieval England and they'd all be up killing the Scotts and the Welsh and the French would laugh at your silly concept that they were all the same race.

This is something that is perhaps difficult to for modern academia to understand but I do feel that the spread of Christianity in Europe was largely responsible for allowing the governments and the church to erase the various racial distinctions of the Romans vs the Gauls vs the Germanic tribes and lump them all together as having the same "souls" and therefore all being equally human. The Romans were pretty smart to seize upon the opportunity and spread it throughout their empire as a means to help enforce cohesion rather than having a varied pantheon of gods many of which would be considered the national deity of whatever tribe you were trying to subjugate. One of the reasons why the reformation was such a great historical event in Europe as it essentially shattered the remnant of the Roman empires control over Europe.