What does this required empty parameter mean, when defining something? - latex

Question

\newenvironment{nameOfEnvironment}[1][]%
Can someone explain the empty bracket?

Answer 1

You should consider reading Is there a comprehensive and complete LaTeX reference? where you'll find information on all sorts of LaTeX2e sources.
Technically, \newenvironment{<cmd>}[<num>][<default>]{<beg-def>}{<end-def>} uses \newcommand as base, so understanding the latter will help you understand the former.
Specific to your case, LaTeX2e for authors user guide mentions the following about \newcommand:
...the command:
\newcommand{<cmd>}[<num>][<default>]{<definition>}
defines <cmd> to be a command with <num> arguments, the first of which is
optional and has default value <default>.
Note that there can only be one optional argument but, as before, there can be
up to nine arguments in total.
So,
\newenvironment{nameOfEnvironment}[1][]%
{<beg-def>}
{<end-def>}
defines an environment nameOfEnvironment that takes a single argument (as a result of [1]). This single argument is an optional argument (as a result of the second []) that, if not specified, has an empty default value.
You would be able to use it as
\begin{nameOfEnvironment}
<stuff>
\end{nameOfEnvironment}
or
\begin{nameOfEnvironment}[something]
<stuff>
\end{nameOfEnvironment}
In the former case, the optional argument #1 is empty, while the second has an optional argument value of something.
The following explanation is taken from LaTeX: Structured documents for TeX (unofficial LaTeX reference manual):
13.5 \newenvironment & \renewenvironment
Synopses:
\newenvironment[*]{env}[nargs][default]{begdef}{enddef}
\renewenvironment[*]{env}[nargs]{begdef}{enddef}
These commands define or redefine an environment env, that is, \begin{env} ... \end{env}.
*
The *-form of these commands requires that the arguments (not the contents
of the environment) not contain multiple paragraphs of text.
env
The name of the environment. For \newenvironment, env must not be
an existing environment, and the command \env must be undefined. For
\renewenvironment, env must be the name of an existing environment.
nargs
An integer from 1 to 9 denoting the number of arguments of the newly-defined
environment. The default is no arguments.
default
If this is specified, the first argument is optional, and default gives the default value for that argument.
begdef
The text expanded at every occurrence of \begin{env}; a construct of the form #n in begdef is replaced by the text of the nth argument.
enddef
The text expanded at every occurrence of \end{env}. It may not contain any
argument parameters.