So, there's an "I approve" rep option, which is green.
There's also an "I Disapprove" rep option, which is red.

I was looking through my posts, and I noticed a few gray ones. What are these gray boxes indicators of?

Gray ones mean that you were either plus repped or minus repped by someone with absolutely no rep power at all. They have no green boxes, their rep can't affect you. You'll just have to figure out what they mean from what post they repped and their reason/comment. Hope that helps.

Thanks for the help