Statistics: Rao-Blackwell Theorem

http://www.geocities.com/asdfasdf23135/stat4.JPG

I was reading this theorem again and again, but I really don't understand the meaning of "for all theta" in this theorem (circled in red). I thought that theta is supposed to be an unkown CONSTANT. Then how would it make sense to say "for all theta"? How would it change the theorem if the "for all theta" wasn't there? Why is this "for all theta" absolutely necessary?

[If it were to say "for all theta hat", then it would at least make some sense to me since theta hat is a random variable...at least it's a variable and it makes sense to talk about "for all", not a constant like theta]

Could someone please explain? Thank you for any help!