When I click play on Battleblock Theater it says:
You are not connected to steam item sever, you will not able to unlock or trade items.
I just don't know how it work.
This error could be caused by multiple things.
It might just be a problem with Steam. Sometimes the item server goes down unexpectedly on various other games including this one. (Steam gauges is a good website to check for Steam servers however Battleblock Theater is not on there.) My advise would be to try again in an hour or wait for a day.
Could it be your anti virus or anti malware blocking it? Try adding this game to your exceptions on whatever anti virus/malware you use.
You should still be able to play your game, It's just that you wont be able to receive or unlock any items you would normally be able to achieve.
You should also see this, it tells you about the consequences of playing offline (which is essentially what you are doing when you get this message but continue to play) in Battleblock Theater.