why a protein domain fold independently? - (Nov/23/2015 )

i was reading about protein domains and i asked myself, how scientists know or recognize them?

the definition of domain is ,it can be independently folded and exist independently,  but what mean it?, perhaps it means that one domain is not covalently attached with the other ones, 

would i say that all domains show enzymatic activity?

I think that all that is meant here is that the domain can be expressed by itself and will spontaneously fold into the "correct" shape without interaction from the rest of the protein. This does not imply activity of the domain, merely that it form the same shape as it would in conjunction with the rest of the protein.