Perché is translated as either why or because:
Perché non mangi? - Why aren't you eating?
Perché non ho fame - Because I'm not hungry
More rarely, it translates in order to. There's a famous quote that goes:
Non sono d'accordo con quello che dici, ma darei la vita perché tu possa dirlo - I don't agree with what you're saying, but I'd give my life in order for you to say it (That possa belongs to the subjunctive tense of potere; if you haven't already, you will study it later in the course!)
Poiché can be used as a formal synonym for because:
Non ho mangiato nulla, poiché non avevo fame - I didn't eat anything because I wasn't hungry
You can't use it in questions to translate why:
Poiché Perché non mangi?
You can't use it to translate in order to:
poiché perché tu possa dirlo
Unlike perché, it can be used to translate since in sentences like:
Poiché non avevo fame, non ho mangiato nulla - Since I wasn't hungry, I didn't eat anything
You can begin this sentence with poiché, but not with perché. A synonym for poiché is siccome. Siccome is used in subordinate clauses that precede the main sentence.
In the end, you'll have these alternatives:
Poiché/siccome non avevo fame (sub), non ho mangiato (main)
Non ho mangiato (main), poiché/perché non avevo fame (sub)
Hope this helps!