Glossary
Space
In one line: Gaining ground on the map by pushing forward, so the team has more room and more options.
What it means
Taking space means pushing your team's line forward: occupying a part of the map that belonged to the enemy, or that nobody controlled. The more space you have, the more cramped the enemies are and the more options you have.
On attack, space is taken with utility and players moving up together; on defense, you deny it with a contest or utility. "Making space" for teammates is also the entry's job: drawing the defenders' attention so the others can get in.
An example
On attack your duelist pushes halfway up main behind a smoke and a movement ability, and the defense falls back. Now the rest of the team can get there safely and decide where to go from there.