This symbol has a square in the middle, triangles on the sides, and arrows in the corners. What does it mean?

Since no-one has a good guess, here is how I would try to track it down.

1. Turn off Time Machine
2. Reboot the mac
3. open terminal
4. run this command sudo fs_usage -w
5. let fs_usage run for a bit and make sure all disk access is to a minimum,
6. repeat the steps to make that icon appear - noting the time to the second
7. press ⌃-C to kill the fs_usage dump and scroll back to see what application or files were being read when the icon appeared.

Posting a guess in case it helps someone else figure out the answer.

I've now looked at nearly every icon on my Lion MacBook Pro, and a lot of the PNG's too. I have found most of what I expected to find but still not this symbol.

My guess is that your icon is related to the iMac going into or coming out of target display mode. Perhaps it was trying to go into target display mode but you didn't have anything connected and this was how it was complaining about there being no signal. It is a known problem with iMacs that they can erratically go into target display mode when the SMC is having problems.

So far, the closest I have found is

which is obviously different, but close. It is for changing a slide show to fit-to-screen mode.