Great question, and there are some great answers here already. Here's what I would add:
Learn more about your boss's job, how their own success or failure is measured, and then align your efforts with theirs.
One of my first jobs was scooping ice cream and making smoothies on this little shack on the beach. Scooping ice cream is pretty easy, but making a good smoothie takes a bit of skill. After 30 or 40 of them, I was pretty good. I kept things clean, and my boss seemed to think I was doing a good job.
A little while after that, another person was hired. He did all the stuff that I did. But he also understood that this was a business. For me, I was just trying to make some extra money. For him, he was trying to further the overall success of the business. He asked about our inventory, because you can't make smoothies without ingredients. He looked at our signage out front, because people won't come in if they don't know what we're selling. He payed attention to peak hours, to make sure we were ready for them.
And I was... making some pretty good smoothies, trying to make some money.
Guess who got a promotion after one month (and was thus making more money)? Not me.
Figure out what your boss cares about, and then align your efforts to help meet their definition of success.
Hope that helps!