Three possible reasons:
1) We don't like the glare. If our phone is sitting on a coffee table it will sometimes catch glare from the television or the window. And that's not cool.
2) We are easily distracted by push notifications. So, to be respectful to you and other people, we put our phones face down so that we don't keep checking in.
3) We are cheating on you and we don't want you to see the text messages from the myriad of women we are cheating on you with.
I sincerely hope that your boyfriend falls into one of the first two categories. I'm 99% sure he does.