What does "awake" mean? I obsessively check the battery info on my ICS phone, and I've noticed that I get the best battery life when the phone hasn't been "awake" much.  But I realized I don't really know what "awake" means.  I have not found a definition for it, and frankly am too lazy to download and grovel the SDK docs.

So ... what precisely does "awake" mean?
This is a power consumption thing. Most time when you're not using a smartphone it's in suspended state. I.e, as many as possible components are off and don't consume power. Awake means the CPU is in the running state. This usually means you're using it and the screen is also on.

Android devices also regularly wake up to check email, push notifications and so on even when thescreen is off. Also playing music or using navigation both with screen off forces the cpu to be awake.

Hence your finding: More awake -> more battery drain