How to customize Beamer "definition" environment?

These definitions come from the amsthm package which is loaded by beamer.

So you can define your own "definition" adding these lines to your preamble:

\theoremstyle{definition}
\newtheorem{mydef}[theorem]{定理}

Now, instead of

\begin{definition}{定理}
 A \alert{prime number} is a number that has exactly two divisors.
\end{definition}

write

\begin{mydef}
 A \alert{prime number} is a number that has exactly two divisors.
\end{mydef}

and you will have:

You can change the \theoremstyle to plain or example to get different appearance.

Do you want to define a new environment with command using Chinese characters "定理", or just want the environment title appear differently? For the latter, add

\theoremstyle{definition}
\newtheorem{dingli}{定理}

to the preamble, so that

\begin{dingli}
A \alert{prime number} is a number that has exactly two divisors.
\end{dingli}

will give you

If, however, you want to use command \begin{定理}\end{定理} instead. Then you will need to typeset with engine that provide full support for Unicode characters, such as XeTex. In that case you have to use package xeCJK instead of CJK.