Depending on whether you want to use the label in place of the x tick label, or as additional information to each bar, here are two approaches.
You can use the key xticklabels from table={<table or file name>}{<column name>} to specify which column to read the labels from. These will be displayed instead of the x-coordinates of the bars. Note that you should also use the option xtick=data (keyword "data" is an in-built) to make sure that ticks are only created in those positions where a bar is drawn.
If you want to keep the x tick labels, you can add the textual labels at the top of each bar by using nodes near coords. This will add a text node above each bar, which will contain the meta data for that point. By default, this is the y coordinate. You can specify which column to use for the meta data by using meta=<column name> as an option to the table keyword. Note that for text data, you have to provide the option point meta=explicit to the plot, otherwise numerical data is expected.

\documentclass{article}
\usepackage{pgfplots}
\usepackage{filecontents}
\begin{filecontents}{testdata.dat}
Label X-Position Height
A 1 15
B 2 20
C 3 12
D 4 24
\end{filecontents}
%
\begin{document}
\begin{tikzpicture}
\begin{axis}[
ybar,
xtick=data,% crucial line for the xticklabels directive
ymin=0,
xticklabels from table={testdata.dat}{Label}
]
\addplot table [
x=X-Position,
y=Height
] {testdata.dat};
\end{axis}
\end{tikzpicture}
%
\hspace*{0.5cm}
%
\begin{tikzpicture}
\begin{axis}[
ybar,
xtick=data,
ymin=0
]
\addplot +[
nodes near coords,
point meta=explicit symbolic
]
table [x=X-Position,
y=Height,
meta=Label
] {testdata.dat};
\end{axis}
\end{tikzpicture}
\end{document}