Illegal parameter number in definition

The error message means what it says. In the simple case, you’ve attempted a definition like:

\newcommand{\abc}{joy, oh #1!}
or (using TeX primitive definitions):
\def\abc{joy, oh #1!}
In either of the above, the definition uses an argument, but the programmer did not tell (La)TeX, in advance, that she was going to. The fix is simple — \newcommand{\abc}[1], in the LaTeX case, \def\abc#1 in the basic TeX case.

The more complicated case is exemplified by the attempted definition:

\newcommand{\abc}{joy, oh joy!%
  \newcommand{\ghi}[1]{gloom, oh #1!}%
will also produce this error, as will its TeX primitive equivalent:
\def\abc{joy, oh joy!%
  \def\ghi#1{gloom, oh #1!}%
This is because special care is needed when defining one macro within the code of another macro. This is explained elsewhere, separately for LaTeX definitions and for TeX primitive definitions