A vector is a mathematical object that has both a magnitude (size or length) and a direction. In game development vectors are used everywhere — representing positions, movement directions, velocities, forces, and distances between objects all use vectors under the hood.

In 2D games you work with Vector2 which has an x and y component. In 3D games you use Vector3 which adds a z component. Think of a vector as an arrow pointing from one place to another — the arrow's length is the magnitude and the way it points is the direction.

Coordinate systems are how games map positions in space. Most 2D environments use a simple grid where x increases to the right and y increases either up or down depending on the engine — this difference catches people out constantly. Pico-8 and most 2D engines have y increasing downward (screen coordinates), while mathematical convention has y increasing upward.

Understanding a handful of core vector operations opens up an enormous amount of game logic — moving towards a target, keeping objects within bounds, detecting proximity, launching projectiles, and smooth camera follow all come down to basic vector math.