What does being engaged at work really mean?

It's an attitude. If you are primarily working for a paycheck, you are not engaged. If you are a clock watcher, then you are not engaged. When you are interested in the work, can suggest ways to improve the situation, and are motivated to help the company succeed, then you are engaged.

It is like when you see puzzles with gears. One lone gear spinning by itself is just that, one lone gear. Machinery does not work well without all the parts meshing together. In the same way, engagement at work is when you do your part in conjunction with all the other workers.

If you do your job well and with efficiency, you are engaged in it. If you dread going to work and it is a chore to even get up to go to it, then you are not engaged in the work. If this is the case, then perhaps the best solution is to find other employment. Satisfaction is also key to being engaged at work.