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}