You could manually alter the shape of the font using \upshape. Or, you could redefine what \itshape (switching to italic font) means by letting it default to \upshape. The latter is possible using a patch provided by the [etoolbox package][etoolbox-pkg]. However, even though the change will be local to the environment, other \itshape uses will also be made to \upshape. Perhaps this isn't a concern in this case.

\documentclass{article}
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\newenvironment{definition}%
{\itshape}% \begin{definition}
{}% \end{definition}
\begin{document}
% Normal definition
\begin{definition}
This is a definition, in which I would like to have a few normal words.
\end{definition}
% Manually corrected definition
\begin{definition}
\upshape This is a definition, in which I would like to have a few normal words.
\end{definition}
\AtBeginEnvironment{definition}{\renewcommand{\itshape}{\upshape}}% You can also place this in your document preamble
% Automatically corrected definition
\begin{definition}
This is a definition, in which I would like to have a few normal words.
\end{definition}
\end{document}