"Be not Conformed
to this world "

means,
Do not be like this world. 
Do not be like this world in manners, opinions, or moral qualities.  Do not live
or act according to this world.
 

"To be Conformed to",
means,

Be like, or be made alike to.
To be alike in manners, opinions,
or moral qualities.  To yield to,
or obey; to live or act 
according  to. 
I beseech you therefore, brethren,
by the mercies of God,
that you present your bodies a living sacrifice,
holy, acceptable unto God,
which is your reasonable service. 
And be not conformed to this world:
but be ye transformed by the renewing of your mind, that ye may prove what is that
good, and acceptable, and
perfect, will of God.

Romans  
12:1-2