Range is a measurement used to determine how far a basic attack or skill can reach. MOBA tends to describe that distance in a vague measurement of "units". It shares the scale of "units" with movement speed, so one point translates to one game distance unit traveled. Note that basic attack range is measured differently to skill range. Given a source unit's hitbox and a target unit's hitbox, range is calculated as follows: basic attack range from edge to edge; targeted skill range from center to center; skillshot range from edge to edge; and the range of self-centered area of effects are from the edge of the source (the larger heroes don't benefit less from auras than smaller heroes). The difference is approximately the model size of the target.
Each hero begins the game with a particular base basic attack range. This can vary from 100 to 400 for melee units and 400 to 680 for ranged units. The highest base autoattack range for heroes is held by Usopp (580). Without active abilities, the highest autoattack range is 644 held by Doma Umaru at level 18. With active abilities, the highest autoattack range is 680 held by Kaname Madoka with level 4 of Lamination of Cause & Effect [E].