What does it mean when your boyfriend hides his phone?

Well, he most likely is hiding SOMETHING from you. It could be incoming/outgoing calls, texts, pictures, etc. Be wary of this, but don't overreact. I know that if *I* had even the slightest shady text on my phone (that is completely innocent, but be construed as otherwise), I too would hide my phone.
Don't be sneaky, and go through his phone. Simply ask to see it, and be upfront. Let him know you're feeling suspicious or insecure, and offer to show your phone as well. Keep lines of communication open.