Spacing describes both a player's awareness of an opponent's options and said player's ability to avoid and counter them. At its simplest form, spacing tests knowledge of how characters can move before, during, and after an action, and the periods of vulnerability and invulnerability of those actions. Every action in game has a certain timing and area of effect; to "space around" an action means to use knowledge of both its timing and range to pick the appropriate option to counter it. Spacing is an integral skill needed to succeed in competitive Smash, as every single interaction is decided by who picked the better timing and position in an exchange of actions.
At the lowest level of competitive play, spacing only involves superficial comparison of the hitbox ranges of attacks with very little nuanced timing due to lack of tech skill and knowledge of positioning. At this level of play, the most successful characters tend to be characters with long raw hitbox range like Marth, or characters with fast attacks such as Sheik. As the level of play increases, players first reach a level of tech skill where they are able to extrapolate how hitboxes can move relative to their character's movement. At this level of play, players are able move in and out of attack ranges, albeit fairly imprecisely, with simple movement options like wavedashing and dash dancing. At the highest level of play, players have internalized the knowledge of their character's movement and attacks to where they can move around attacks at very precise distances; the example at the beginning of the page demonstrates very precise awareness of the range and timing of Sheik's shield grab.