"Spacetime", (aka "the spacetime continuum", but no scientists actually use this term), is an important-sounding name for something that is so obvious it's confusing except for one very surprising and mindbending fact.
Every physical process in the universe happens at a place (or multiple places) and time (or multiple times). "Spacetime" is the name for the possible places and times. That's the part that's so obvious it's confusing.
The surprising part is that spacetime has a WEIRD SHAPE.
Physicists often visualize spacetime as like x, y, z, and t axes, and you've probably done that in math and science classes (or maybe you've at least done part of spacetime, like slices with x and t directions). That collection of axes has a shape: it's basically an infinite cube (except 4-dimensional).
Turns out that "naive" guess at the shape of spacetime is WRONG. Well, it's often a convenient approximation so it's used very frequently, but it's not precisely accurate.
The actual shape of spacetime is bizarre. Distances along lines that extend in the t direction are DIFFERENT than distances along lines in any other direction, and the way those distances are measured must CHANGE with the angle the line makes with the t axis.
Worse, if there are objects in spacetime, the region of spacetime near that object will WARP. Basically distances near objects must be measured differently than distances away from objects, and the more massive the object, the more different the distances will be from what you'd expect.
Summary: spacetime is just a name for the collection of all possible places and times that physical events can occur in, but people make a big deal out of it because if you try to visualize it as a shape like physicists often do, the shape that is physically accurate is actually very surprising.
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