1. to separate an area from the rest of sth
box off a room/area/section
To 'box something off' is to separate something from other things or another area: "We should box off the sculptures from the interactive pieces to prevent any damage to the artwork." You can 'box off' a room, an area or a section of something. This can be used in social or professional contexts and is similar to the phrases 'to enclose' or 'to tape off.'
2. complete a task and leave free for another
get the project/task/assignment boxed off
To have something ‘boxed off’ means that you have it completed or finished. This is a more colloquial use of this term but can be used in professional settings. Similar in meaning to ‘tick the box’.