> Does it mean when a cable is pulled through on a piece of string?

That is often exactly what is meant. The problem of running Ethernet through existing structures has spawned a bunch of tools, including glow-in-the-dark "fish tape."

The process is often brutal, and looks like tug-of-war when it takes a couple men to pull the bundle through a couple 90 degree turns. As such, we have "plenum" cable, which is much tougher than typical patch cable, because the latter would just get shredded inside the structure, or snap when pulled with a few hundred lbs of force.