For or fordi

For presents an explanation, that is: it gives you enough information to understand the situation. Fordi gives a reason, which means telling you what lies behind the situation. In most cases you can use for or fordi with no big difference in meaning - the reason may be a good explanation. But in some cases - especially after ikke and in complex periods - it becomes unclear what the reason is reason for:

Han røg ikke, fordi han var nervøs. (He did not smoke because he was nervous) is no good sentence - it may be read in two ways: Either: He was nervous, so he did not smoke. Or: He did smoke, but not because of his being nervous. So watch out after ikke.

Other constructions/meanings that call for the word for are conclusions based upon what you see, and complex phrases where the reason refers to the first part of the sentence:
Jeg tror, han har røget i sengen, fordi ilden startede i soveværelset. (I think, he has been smoking in his bed, because the fire has started in the bed room.) Again the phrase can be read in two ways.
For carries the same meaning as for in written and 'cause in spoken English.
Jeg tror, at han gemte sig under sengen, han var bange.
Jeg tror, at han har gemt sig under sengen, jeg synes, jeg kan se hans sko.