What exactly is it that you're confused about? It's not clear from your post what parts you do and don't understand.
The basic facts in a nutshell are:
1) If you are an American citizen, you are subject to being taxed on your income regardless of where you earned it
2) Based on certain factors (time spent physically being outside of the US, establishing "residence" (a term with a very specific definition for IRS purposes)) you may be able to exclude part or all of your foreign-earned income from US taxation
3) In certain circumstances, you may be able to request an extension on filing taxes (not necessarily an extension on paying, if you should owe) in order to meet those certain factors to exclude your foreign-earned income.
A person's tax issues are like his/her medical health - there are general guidelines and governing concepts that apply to everyone, but the specifics and prescriptions for each case is unique to the individual.
The best information comes straight from the source "Tax Guide for U.S. Citizens and Resident Aliens Abroad" :
http://www.irs.gov/publications/p54/index.htmlIf you're still unsure you'll either want to see a tax preparer in your area with expertise in US taxation for those living abroad or use a tax preparation program (like TurboTax) combined with some reading and research on your part.
Standard disclaimer here: I am not a tax attorney, nor do I play one on TV, and I did not stay in a Holiday Inn Express last night.