A “continuum” is a thing that is “continuous”, meaning that each part is right next to another part, and broadly similar to it.
The normal numbers are a continuum. Give me any number and I can find another number as close to it as I like. And those numbers behave in similar ways.
In some physics models “space” is a continuum – each bit of space is right next to more space, and space generally looks the same wherever you are. Since the early 20th century physics has tended to combine space and time into a single continuum, modelling time as something similar to space, and overlapping it in some situations (in General Relativity one of the ways of understanding why things “fall” because their local “forwards through time” direction overlaps the wider “down” direction).
The term “continuum” isn’t used that much in physics to refer to spacetime (although it does get used in some other areas, like continuum mechanics, which is the study of how objects or systems deform – when you treat them as a single continuous thing rather than being made up of individual particles); generally rather than talking about the “spacetime continuum” we’d just talk about “spacetime.” It is one of those terms that gets used a lot in science fiction, though, as it sounds fancy.
Basically it means everything. All of space and all of time.
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