I am thinking it would be due to a evolution of conversation, such as a conversation flows better with a close friend as opposed to somebody you have just met.  Reading body language is another example of this, the more you know the person the more you can understand their body language. 

From a neuroscience perspective I wonder what the use of hallucinogens would play in allowing this form of communication to happen, presuming it is telepathy and not some greater understanding/tripping balls kinda thing...

Speaking to the pastor (he has two PhDs) where I go to church awhile back and got onto this topic.  From a theological point of view, he believes in the resurrection of the body, and was stating that some christian scientists believe the human brain has the capacity for telepathy, and that this would be available after death.  I will see if I can get a hold of any scientific articles that can confirm this.