The report document class provides \chapter (and more), just like the book document class. And, as a consequence, it defines all sectional heading numeration relative to this commonly-used top-level sectional heading \chapter. Yes, there is another level higher called \part, but that is not used that often.
Numbered section titles have \thechapter.\arabic{section} by default; numbered subsection titles have \thesection.\arabic{subsection}; etc. This defines a hierarchical numbering structure, which is typical from what you see in books. Overriding this is possible by merely removing the chapter counter from being printed with the section counter:
\renewcommand{\thesection}{\arabic{section}}
The \the<counter> refers to the printing of the counter <counter>. The above command changes that printing behaviour to just print the section counter using the \arabic style. Since all the lower-level sectional counters print using the hierarchical structure, only this definition is needed for the rest to work as expected.
A better (perhaps preferred) alternative to this is to use a document class that does not support chapters. This is provided by the article document class. Since it does not provide \chapter, \section is the top-level sectional heading, making all counters necessarily be numbered hierarchically according to it.
\documentclassdo you use? – Vlad Oct 20 '11 at 23:21