A spacetime diagram is a diagram that shows the effects of special relativity.
Spacetime diagrams are often used to validate relativity (by demonstrating that the paradoxes of relativity are not actually paradoxes.) However, the whole concept of the spacetime diagram is constructed from relativity itself. Therefore, the logic is circular; spacetime diagrams do nothing to prove relativity.
Suppose two reference frames, S and S' . Suppose S is stationary, and S' is moving at velocity v.
The vertical axis of the spacetime diagram is ct (speed of light multiplied by time) and the horizontal axis is x (position). The horizontal and vertical axes of the reference frame S' are denoted ct' and x' and are tilted inward (as seen below.)