Inserting an image properly in a table

Similar to the solution I provided in How to draw arrows between parts of an equation to show the Math Distributive Property (Multiplication)?, you can use \tikzmark as defined in Adding a large brace next to a body of text. Each endpoint of the line is identified by \tikzmark, and the \DrawLines macro draws the line between each of the nodes.

You can adjust the shorten <=<size> parameter to start the lines a little later which achieves a nice effect. Here is the result with shorten <=7pt:

Curved lines can also be obtained by specifying in=<angle> and out=<angle> options. For example using \DrawLinesCurved instead of DrawLines you get:

Notes:

• This requires two runs. Once to determine the begin and end point of the lines, and the second to draw them.
• The colors of the 4 lines are passed as parameters to \DrawLines.
• I used the -latex arrows here, but if arrows are not desired this option can be removed.
• I used \raisebox to adjust the position of the text (as requested in the comments).

Code:

\documentclass[12pt]{book}

\usepackage[utf8]{inputenc}
\usepackage[a4paper]{geometry}
\usepackage{graphicx}
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{calc,shapes}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}

\newcommand{\DrawLinesCurved}[4]{%
  \begin{tikzpicture}[overlay,remember picture,-latex,shorten >=1pt,shorten <=1pt, thick]
    \draw[out=80,  in=180, #1] (a.north) to (b.north west);
    \draw[out=40,  in=180, #2] (a.north) to (c.north west);
    \draw[out=320, in=180, #3] (a.north) to (d.north west);
    \draw[out=275, in=180, #4] (a.north) to (e.north west);
  \end{tikzpicture}
}

\newcommand{\DrawLines}[4]{%
  \begin{tikzpicture}[overlay,remember picture,-latex,shorten >=1pt,shorten <=1pt, thick]
    \draw[#1] (a.north) to (b.north west);
    \draw[#2] (a.north) to (c.north west);
    \draw[#3] (a.north) to (d.north west);
    \draw[#4] (a.north) to (e.north west);
  \end{tikzpicture}
}

\pagestyle{empty}
\begin{document}

\setlength{\extrarowheight}{5pt}
\raisebox{-12pt}{Foo\tikzmark{a}}\hspace*{1.0cm}
\begin{tabular}[c]{ c c c c c c }
    & A & B & C & D \\ \cline {2-6}
    \tikzmark{b}1 & foo A1 & foo B1 & foo C1 & foo D1 \\
    \tikzmark{c}2 & foo A2 & foo B2 & foo C2 & foo D2 \\
    \tikzmark{d}3 & foo A3 & foo B3 & foo C3 & foo D3 \\
    \tikzmark{e}4 & foo A4 & foo B4 & foo C4 & foo D4 \\
\end{tabular}
\DrawLines{red}{blue}{green}{orange}
\end{document}

\documentclass[12pt]{book}

\usepackage[utf8]{inputenc}
\usepackage[a4paper]{geometry}

\usepackage{graphicx}
\usepackage{multirow}
\usepackage{array,calc,pict2e}

\pagestyle{empty}

\begin{document}

    \setlength{\extrarowheight}{5pt}
\setlength\unitlength{\baselineskip + \extrarowheight}

    \begin{tabular}{ c c c c c c }

        & & A & B & C & D \\ \cline {2-6}
    \multirow{4}{*}{\begin{picture}(1,1)
\put(.5,.5){\makebox(0,0)[r]{foo }}
\put(.5,.5){\vector(2,3){1}}
\put(.5,.5){\vector(2,1){1}}
\put(.5,.5){\vector(2,-1){1}}
\put(.5,.5){\vector(2,-3){1}}
\end{picture}}    & 1 & foo A1 & foo B1 & foo C1 & foo D1 \\
                            & 2 & foo A2 & foo B2 & foo C2 & foo D2 \\
                            & 3 & foo A3 & foo B3 & foo C3 & foo D3 \\
                            & 4 & foo A4 & foo B4 & foo C4 & foo D4 \\

    \end{tabular}

\end{document}

Just to complement Peter's nice answer, I have used the matrix library. This might be of use since you have already typed in the tabular format so I just copied and pasted it.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,calc}
\begin{document}
\begin{tikzpicture}
\matrix[matrix of nodes] (footable) {
   &A & B & C & D \\
1 & foo A1 & foo B1 & foo C1 & foo D1 \\
2 & foo A2 & foo B2 & foo C2 & foo D2 \\
3 & foo A3 & foo B3 & foo C3 & foo D3 \\
4 & foo A4 & foo B4 & foo C4 & foo D4 \\
};
\draw (footable-2-1.north west) -- (footable-2-5.north east);
\node (Foo) at ([xshift=-1cm]$(footable-3-1.west)!0.5!(footable-4-1.west)$) {Foo};
\foreach \x in {2,...,5}{
\draw (Foo) -- (footable-\x-1);%replace (Foo) with (Foo.east) to focus the arrow origins
}
\end{tikzpicture}
\end{document}

So, basically matrix library allows us to type in the tabular data. Then we put a node of which coordinates are calculated by obtaining the middle point of 3rd and 4th rows and shifting it by -1cm on the horizontal axis via calc library. Then a foreach argument draws the lines.