Here's a description Albert Einstein gave on p. 83 of his Relativity: The Special and the General Theory:
The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum
There has been some what of a issue here when I have spoken of two points, and I would like to say that I am using this to reference the space in between, like Q<->Q measure, to signify the energy and curvature implied in this space.
“Distances” Determine Geometry
Describe an object with a table of distances between points.
Describe spacetime with a table of intervals between events
.It is not my purpose in this discussion to represent the general theory of relativity as a system that is as simple and as logical as possible, and with the minimum number of axioms; but my main object here is to develop this theory in such a way that the reader will feel that the path we have entered upon is psychologically the natural one, and that the underlying assumptions will seem to have the highest possible degree of security.
—Albert Einstein
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