The arrow in your example is a cubic Bézier curve, so it has two control points that "guide" the direction of the curve. The position of the first control point is specified by +(south west:5) and the position of the second control point is specified by +(south:5). The following code, adapted from this answer to What type of curve is used by Tikz when I "bend" an edge?, shows these control points for the example you cited.
\documentclass[12pt,a4paper]{article}
\usepackage{tikz-qtree}
\usepackage{tikz-qtree-compat}
\usepackage{ulem}
\def\hcancel#1{}% provissional definition; delete this line in your actual code
\usetikzlibrary{decorations.pathreplacing,shapes.misc}
\tikzset{
show control points/.style={
decoration={show path construction, curveto code={
\draw [blue, dashed]
(\tikzinputsegmentfirst) -- (\tikzinputsegmentsupporta)
node [at end, cross out, draw, solid, red, inner sep=2pt]{};
\draw [blue, dashed]
(\tikzinputsegmentsupportb) -- (\tikzinputsegmentlast)
node [at start, cross out, draw, solid, red, inner sep=2pt]{};
}
},
postaction=decorate
},
}
\begin{document}
\begin{tikzpicture}
\Tree
[.{$<$t${1}$,\hspace{0.1cm} \$\lbrack$ \hspace{0.3cm} $\rbrack$, $\lbrack$ \hspace{0.3cm} $\rbrack$ $>$}
[.{$<$(e${3}$ $\rightarrow$ t${1}$) $\rightarrow$ t${1}$),\hspace{0.1cm} \$\lbrack$ e${3}$ $\rbrack$ $>$} \node(wh){something} ;
]
[.{$<$(e${3}$ $\rightarrow$ t${1}$), \hspace{0.1cm} \$\lbrack$ e${2}$ $\rbrack$, \hspace{0.1cm} \$\lbrack$ \hcancel{e${3}$}
\thinspace $\rbrack$ $>$ }
[. \node (ue) {e${3}$}; ]
[.\node[draw]{{$<$t${1}$, \hspace{0.1cm} \$\lbrack$ e${2}$ $\rbrack$, \hspace{0.1cm} \$\lbrack$ e${3}$ $\rbrack$ $>$ }};
[.\node[draw]{e${2}$ }; ]
[.{$<$(e${2}$ $\rightarrow$ t${1}$), \hspace{0.1cm} \$\lbrack$ e${3}$ $\rbrack$ $>$}
[.{$<$(e${3}$ $\rightarrow$ e${2}$ $\rightarrow$ t${1}$),\hspace{0.1cm} \$\lbrack$ $\emptyset$ $\rbrack$ $>$} {$<$(e${3}$ $\rightarrow$ e${2}$ $\rightarrow$ t${1}$),\hspace{0.1cm} \$\lbrack$ $\emptyset$ $\rbrack$ $>$}
]
[.\node[draw]{e${3}$ };
[. \node (le) {e$_{3}$}; ]
]
]
]
]
]
\draw[semithick,->,show control points] (le)..controls +(south west:5) and +(south:5) .. (ue);
\end{tikzpicture}
\end{document}

Curves in tikz
More explanation about curves in tikz can be found in the pgf manual, starting with section 2.4 on pp. 31-32. The formal definitions for the options and commands relevant for curves are in section 70.3 on pp. 753-756. There are also many examples of curves throughout the manual and elsewhere on this site.
Coordinates in tikz
You can use any of the tikz systems of specifying coordinates for the control points. These are described in section 11.1 on p. 120 in the manual. In the example you cited, the + means that the control point is specified relative to another point. The first control point is specified to be south west (down and to the left) of the beginning of the curve by 5. The second control point is specified to be south (down) of the end point of the curve by 5. The number is relative to the xy-coordinate system, which by default is measured in centimeters.
These control points could be equivalently specified as +(235:5) and +(270:5) if you prefer working with degrees rather than compass points. They can also be specified as +(-5,-5) and +(0,-5), which allows you to specify both the x- and y-coordinates for the control point for finer control over its position. I personally prefer using these (x,y) coordinates.
{}icon. – Alenanno Jun 18 '15 at 17:51+(south west:5)means a point 5 units from here in the south-westerly direction.+(south:5)means 5 units due south. They are just polar coordinates. You could say e.g.+(-135:5)and+(-90:5). – cfr Jun 18 '15 at 18:05