TiKZ: Why is a line visible between 2 fitted nodes with inner/outer sep =0?

Probably the problem is rendering in viewer (I use Sumatra). If I magnify image obtained with your code, this line disappear. As cure for this viewers discrepancy try the following:

\documentclass{book}
\usepackage{tikz}
\usetikzlibrary{fit}
\begin{document}
  \begin{tikzpicture}%
    [every node/.style =
      {fill=blue, draw=blue, % <-- added "draw"
       inner sep=0mm, outer sep=0mm, 
       minimum width=5cm, minimum height=5cm
      }
    ]
  \node (first) at (10,10) {};
  \node[fit=(first.north) (first.south),anchor=east] (second) at (first.west) {};
  \end{tikzpicture}
\end{document}

Edit: In the Percusse answer is explanation why in your case a thin line between adjacent nodes is visible. Added option draw in above MWE cause, that nodes overlap for thickness of border lines:

consequently there is no more place for image viewer artifacts. Above picture is generated with:

\documentclass{book}\usepackage{tikz}
\usetikzlibrary{fit}

\begin{document}
    \begin{tikzpicture}[
test/.style = {fill=#1, draw=#1, draw opacity=0.5,
               inner sep=0pt, outer sep=0pt, 
               minimum width=5cm, minimum height=5cm}
                        ]
\node (first)  [test=blue]  {};
\node (second) [test=red,
                fit=(first.north) (first.south),
                anchor=east] at (first.west) {};
    \end{tikzpicture}
\end{document}

This effect is generally known as the conflation artifact and it has nothing to do with TikZ. It is a well-known artifact by the graphic designers and they avoid this by avoiding shapes sharing perfectly aligned edges or shapes filling a cut-out exactly.

See for example rendering problems here (wait a bit after you click to see the changes). Similarly graphics.SE has lots of relevant questions and probably the Hillary logo is the most voted one: Is there a reason Hillary Clinton's logo has hidden notches?

So the typical solution is to make things overlap slightly.