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You misunderstand how TeX works. The meaning of a macro can be different in different parts of the document. When TeX reads the document, it does not replace all of '\aWord' in one go. Instead, it reads the file a line at a time. So first it finds
\newcommand{\aWord}{a word}
which defines \aWord ...

Did you try:

Clarification: In the code below:
\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}

\begin{document}
\newcommand{\aWord}{a word}
Testing \aWord
% -- a long document later -- %
\renewcommand{\aWord}{another word}
Testing \aWord
\end{document}
I don't ...

How do I "save" a word in latex' memory? I.e. a word that is given later in the document, how can I use it at the beginning of the document e.g. with newcommand and renewcommand:
\documentclass[10pt,a4paper]{article}
\usepackage[latin1]{inputenc}
\begin{document}
\newcommand{\aWord}{a word ...