What Did Einstein Mean when He Said Space is Curved?

[Alex K]

It's only curved relatively.

I love spoiling jokes so ...

There is such an idea, namely that curvature can be only an artefact of how somrthing is embedded in space, e.g. a piece of paper can be rolled up in space in a curved fashion, but this curvature is not, as they say, "intrinsic", the paper is still intrinsically flat as parallel lines on a rolled up paper keep their distance. This curvature could be called relative. However, the concept of curvature used in Relativity is largely independent of how a space is embedded, and so is not really relative.