This is far too broad of a question to answer on a web forum. The Byzantine era went on for a thousand years, more or less, you won't find any simple answers and entire books have been written about it. You might want to start with this one. There is also a trilogy by John Julius Norwich which are very readable but you have to keep in mind that they are rooted in older Byzantine research that has been superseded.

Do you maybe have something more specific to ask?