It's difficult without knowing how much maths you know. Riemann and others had done a lot of work on the geometry of smooth spaces - more general spaces than the Euclidean plane geometry you probably studied in school. Minkowski apparently recognised that the Lorentz transforms were the same maths that represents "rotations" (typically called boosts, but they are the hyperbolic analogue of rotations) in a type of space now named after him. I don't know if that space was known before Minkowski or if it was his own personal invention. Either way, it's a four dimensional "space" with one dimension that's different from the other three and whose behaviour under boosts matches Einstein's maths. That's spacetime.quote: "these transforms could be interpreted as meaning that space and time were part of one 4d structure, christened spacetime." Would anyone care to expand on this a bit, please?
Note that I believe that other interpretations of the maths are possible. But using geometrical language opens up the whole toolkit of Riemann's differential geometry, so everyone uses that.