four-vector
A four-vector is the natural arrow of spacetime: an object with four components — one for time and three for space — that hang together as a single geometric whole. The most basic example is an event's position, (c t, x, y, z), bundling 'when' and 'where' into one quantity. The point of grouping them is that they transform together as a unit when you switch between observers, in exactly the way the Lorentz transformation prescribes.
Why bother packaging things this way? Because it turns three-dimensional quantities that observers argue about into four-dimensional objects they agree on the structure of. Energy and momentum, for instance, look like two separate things in everyday physics, but relativity reveals them as the time and space parts of one energy-momentum four-vector — just as time and space are two faces of one spacetime. A change of observer that mixes time into space will, in the very same way, mix energy into momentum.
Each four-vector has an invariant 'length' computed with the spacetime minus-sign rule, and that length is the same for all observers even though the individual components are not. For the energy-momentum four-vector, that invariant length is the particle's rest mass — a fixed, frame-independent fact about the particle, while its energy and momentum separately depend on who is watching. Thinking in four-vectors is like switching from describing a tilted stick by its separate shadows to describing the stick itself: the shadows change with the lighting, but the stick does not.
Position is the prototype four-vector; its invariant length is the spacetime interval from the origin.
Not every list of four numbers is a four-vector — it only counts as one if it transforms under the Lorentz transformation the way position does. That transformation rule, not the mere act of stacking four numbers, is what makes the invariant length meaningful.