You are a US citizen by birth:
http://www.uscis.gov/us-citizenship
You are also an Albanian citizen by birth:
https://en.wikipedia.org/wiki/Albanian_nationality_law
Holding US citizenship doesn't cancel out your Albanian citizenship. (See 'Dual citizenship' in my second link, above).
It's possible to lose US citizenship by acquiring citizenship of another country later in life but not by having dual citizenship at birth, so your Albanian citizenship doesn't cancel out your US citizenship:
http://travel.state.gov/content/travel/english/legal-considerations/us-citizenship-laws-policies/citizenship-and-dual-nationality/dual-nationality.html
Therefore you have DUAL NATIONALITY and you're a citizen of BOTH countries, with the respective rights of citizenship of each country.
If you have problems when travelling internationally (other than to either the USA or Albania) BOTH the Albanian Embassy AND the US Embassy can be called upon to assist you. However the Albanian Embassy can't assist you while you're in the USA and the US Embassy can't assist you in Albania.
So, for example, if you were in the USA at a time when US military commitments meant that you could be drafted into the US Army, your Albanian citizenship couldn't be used to prevent that. Similarly, if you were in Albania and called up for compulsory military service, your US citizenship couldn't prevent that.
Any clearer now?