Geometry of light and motion on a single plot
A spacetime diagram (Minkowski diagram) plots time on the vertical axis and space on the horizontal. A stationary object traces a vertical line (its x doesn't change as t increases). A moving object traces a tilted line, with slope 1/v in units where the speed of light is 1. A light ray always travels at 45 degrees (in standard units) because light moves equal distances in space and time. The light cone from an event is the set of all points that can be causally influenced by that event: a future light cone (above the event) and a past light cone (below it). Events inside the light cone can affect or be affected by the event in question. Events outside are causally disconnected.
Relativity and simultaneity reframed
In Galilean relativity, simultaneity is absolute: events at the same time are simultaneous for all observers. In relativity, simultaneity is relative. Two events simultaneous in one reference frame (lying on the same horizontal line) are not simultaneous in another frame (their connection line tilts). A Minkowski diagram makes this clear: when you switch to a moving observer's frame, the time axis tilts, and events that looked simultaneous become separated in time. The speed of light plays the role of the speed limit: no worldline (path through spacetime) can have a slope shallower than 45 degrees. This geometry captures the essence of Einstein's theory without heavy equations.