He means: the guys who take the hire and fire decisions need to know you as a name and aface, not just someone who turns up everyday and collects a salary.
When redundancy time comes around what characteristics do you think mark out the victims from the survivors?
Remember, while engineers make logical rational decisions, most other people (the hire and fire guys, HR. etc) make emotional decisions driven by the ancient fight or flight reflexes. So don't expect to survive simply because you do an honest days work and do it well.
The easiest people to axe are first and foremost those they don't really know and don't have a way to value.... farmers never make pets of the food animals. Next come those who earn the most (despite this probably being because they contribute the most, though this isn't always the case).
It is never enough to just do your job but to be seen to be doing it.
If you receive your jobs from your boss, keep him informed of progress, even a casual comment when passing or a simple paragraph at regular intervals. It helps him keep abs on what you are doing and he begins to know you as a person and a non-threatening one at that. Plus, it is sometimes good to ask for instructions and decisions from him but keep it simple. He will feel comfortably involved. But if all he sees i that you work there and no one actively complains about your work, he may never know what sort of impact it would have to put you on the wrong side of the hire and fire list until it is too late.
By the way, Structural IET, I personally would hesitate about too often declaring my work done and asking for more and you may well be absolutely right.
I, however, would worry that the impression it would create is of never having enough to do and thus being seen as superfluous.... and an easy lay-off. This has never been something I have had to worry about since the status quo has always been too much work required from too few people (what really endears you to management is that when they hire and fire they can get you doing the key parts of two or three peoples jobs for the salary of one) and thus I can't say that it is in fact a bad idea.
JMW