En is a general "in", it can also be used figuratively. Dans is the more literal spatial preposition "in".

In the sentence "to believe in life after death", the preposition "in" is not a literal "inside" and therefore en is the appropriate preposition to use.

Here is another example which demonstrates the difference nicely:

Être en prison. -- to be imprisoned.
Être dans la prison. -- to be inside the prison building (not necessarily as an inmate).

Hi Diane,

you use "que" if what follows is a sentence i its own right. 

Je crois que tu m'as entendu. -- I believe (that) you heard me. Here "tu m'as entendu" is a sentence of its own, therefore "que is needed. 

Je crois en une vie après la mort -- I believe in a life after death. "Une vie après la mort" is not a complete sentence because it lacks a verb. Hence no "que".

This is not unlike in English, where you may use "that" if what follows is a sentence.

-- Chris (not a native speaker)