How to write a perfect equation parameters description?

Define your own environment for this; here I realize it as a two column alignment; the first column is typeset in math mode, the second one in text mode; the = is added automatically, with the correct spacing.

\documentclass{article}
\usepackage{array}

\newenvironment{conditions}
  {\par\vspace{\abovedisplayskip}\noindent\begin{tabular}{>{$}l<{$} @{${}={}$} l}}
  {\end{tabular}\par\vspace{\belowdisplayskip}}

\begin{document}
An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
where:
\begin{conditions}
 P     &  notional permeability factor \\
 N     &  number of waves \\   
 S_{d} &  damage level
\end{conditions}

\end{document}

If your conditions are overlong, then you can use a different environment, that I call conditions*, based on tabularx:

\documentclass{article}
\usepackage{tabularx}

\newenvironment{conditions*}
  {\par\vspace{\abovedisplayskip}\noindent
   \tabularx{\columnwidth}{>{$}l<{$} @{${}={}$} >{\raggedright\arraybackslash}X}}
  {\endtabularx\par\vspace{\belowdisplayskip}}

\begin{document}
An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
where:
\begin{conditions*}
 P    &  notional permeability factor and something 
          longer that needs to be taken at the next line\\
N     &  number of waves \\
S_{d} &  damage level
\end{conditions*}

\end{document}

---

Variant for variable symbols

If different symbols are needed instead of = in each line, here's how.

\documentclass{article}
\usepackage{array,tabularx}

\newenvironment{conditions}
  {\par\vspace{\abovedisplayskip}\noindent
   \begin{tabular}{>{$}l<{$} @{} >{${}}c<{{}$} @{} l}}
  {\end{tabular}\par\vspace{\belowdisplayskip}}

\newenvironment{conditions*}
  {\par\vspace{\abovedisplayskip}\noindent
   \tabularx{\columnwidth}{>{$}l<{$} @{}>{${}}c<{{}$}@{} >{\raggedright\arraybackslash}X}}
  {\endtabularx\par\vspace{\belowdisplayskip}}

\begin{document}
An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
where:
\begin{conditions}
 P     & =       &  notional permeability factor \\
 N     & \sim    &  number of waves \\
 S_{d} & \propto & damage level
\end{conditions}

An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
where:
\begin{conditions*}
 P     & =       & notional permeability factor and something 
                   longer that needs to be taken at the next line\\
 N     & \sim    & number of waves \\
 S_{d} & \propto & damage level
\end{conditions*}

\end{document}

---

In order to have no break after “where:”, here's a variant of the first solution:

\documentclass{article}
\usepackage{array}

\newenvironment{conditions}[1][where:]
  {#1 \begin{tabular}[t]{>{$}l<{$} @{${}={}$} l}}
  {\end{tabular}\\[\belowdisplayskip]}

\begin{document}
An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
\begin{conditions}
 P     &  notional permeability factor \\
 N     &  number of waves \\
 S_{d} &  damage level
\end{conditions}
Some text after the equation.

\end{document}

The conditions environment has an optional argument for changing the fixed where:; so, for instance, \begin{conditions}[with:] will use “with:”.

A different version that allows for longer descriptions that needs to be wrapped across lines:

\documentclass{article}
\usepackage{array,tabularx,calc}

\newlength{\conditionwd}
\newenvironment{conditions}[1][where:]
  {%
   #1\tabularx{\textwidth-\widthof{#1}}[t]{
     >{$}l<{$} @{${}={}$} X@{}
   }%
  }
  {\endtabularx\\[\belowdisplayskip]}

\begin{document}
An equation just to start
\begin{equation}
P+N=S_{d}
\end{equation}
\begin{conditions}
 P     &  notional permeability factor with some more text
          so this ends up to break across lines blah blah
          blah blah\\
 N     &  number of waves \\
 S_{d} &  damage level
\end{conditions}
Some text after the equation.

\end{document}

As daleif suggested you could use the align* environment. You get the alignment just like in tables with '&'. Here is an example:

\documentclass{article}
\usepackage[fleqn]{amsmath}
\begin{document}

\begin{align*}
    H_s &= \text{significant wave height, equal to the average of the highest 1/3 of
    the waves}\\
    \Delta &= \text{relative buoyant density, equal to }\rho_r\text{ / }\rho_w - 
    1\text{, where }\rho_w\text{ is the water density}\\
    D_{n50} &= \text{nominal  diameter defined in Equation \eqref{eq:dn50g50}}\\
    P &= \text{notional permeability factor}\\
    S_d &= \text{damage level}\\
    N &= \text{number of waves}\\
    \xi_m &= \text{breaker parameter based on mean wave period }T_m\\
    \alpha &= \text{slope angle}
\end{align*}
\end{document}

This should work for you. This is the output:

If you don't want all equations to be aligned left, you can use the flalign* environment, like suggested here.

Another option is to use the tabbing environmnent:

\begin{equation}
\frac{H_s}{\Delta D_{n50} } = 1.0~ P^{0.13}~ \left(  \frac{S_d}{N} \right)^{0.2}  \xi_m^P~ \sqrt{\cot \alpha}
\end{equation}
where: 
\begin{tabbing}
\phantom{$D_{n50}\ $}\= \kill
$H_s$\> = significant wave height, equal to the average of the highest 1/3 of the waves\\
$\Delta$\> = relative buoyant density, equal to $\rho_r / \rho_w - 1$, where     $\rho_w$ is the water density\\
$D_{n50}$\> = nominal  diameter defined in Equation \eqref{eq:dn50g50}\\
$P$\> = notional permeability factor\\
$S_d$\> = damage level\\
$N$\> = number of waves\\
$\xi_m$\> = breaker parameter based on mean wave period $T_m$\\
$\alpha$\> = slope angle\\
\end{tabbing}

The first line in the tabbing environment will set the spacing (i.e. tabstop). The \kill command suppresses the line it precedes, otherwise you would have an extra space between 'where:' and the first definition.

Alternatively, instead of \phantom{$D_{n50}\ $} (the longest item on your list), you can use a fixed width: \hspace{3cm}.