Space  Time ( or Spacetime ) Fabric
( Or What Exactly is It? )
"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity"  by Alan Turing ( 1912  1954 )
1). In Special Relativity:
( no gravity )
The universal constant speed of light in pure vacuum, interstellar outer space dictates, as a function of a body's velocity relative to , the ( geo ) metric length of a unit rod for measuring all other space  distances. And, the pace of any clock progression ( or the "light doppler effect" ) operationally defines the meaning of time. Both of these concepts of 'space' and 'time' are brought together in the unified concept of "space  time ( or spacetime ) fabric" as mathematically revealed by the FitzGerald  Lorentz Transformation Equations:
2). In General Relativity:
( gravity )
Both the ( geo ) metric unit rod lengths for measuring all other space  distances and the unsteady progression of clocks are warped by gravity's varying fields of force. This physical phenomenon again constitutes the concept of "space  time ( or spacetime ) fabric" from spacetime point  to  spacetime point as mathematically revealed by Einstein's ( EFE ) Gravitational Field Equation:
Summary
Now, in any given amount of volume of space, a "unit" rod of measure, which defines the metric for space, will differ from some other "unit" measuring rod as set against the universally constant speed of light taken in whatever arbitrary volume of space is given, while also remembering that a beam of light itself ( i.e., lightsecond, lightyear, etc. ) measures distances between event  points in space.
However, the relations of distances taken in any given amount of volume of space between "unit" measuring rods traveling at different relative velocities to one another as given by
outline the undulations ( dilations & contractions ) of space ( spacetime ) "fabric", to use this commonly accepted latter metaphor for cloth!
So, therefore, not only does each event  point in space possess a unique progression rate of clock  time but, also, space ( spacetime ) itself when objectively viewed from different relative event  points of view and depending upon relative velocities and energy fields of accelerating gravity, will dilate ( expand ) and contract as demonstrated by "unit" rods of measure, thus forming a sort of metaphorical fabric cloth of spacetime.
In other words, what relates each of these unit measuring rods to one another are the very same Special Relativity equations for length dilations and contractions as already given:
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