What does documenting in ‘real time’ mean?

Real time documentation would be documenting as the incident is occurring; i.e., taking minutes on a computer and posting for use as the meeting is held, or writing a process as the process occurring, like writing a recipe as you make the food.

Depends on the context. I agree with the previous comments, but would add that it can also mean documenting your own work processes as you tackle them. Keeping a running tally (often using Outlook, or another calendaring tool, but sometimes just a piece of paper) and indicating start/stop on specific tasks, functions as they are done.