The new list of definitions was created using the LaTeX's kernel \@starttoc and it behaves in the same way as the standard LoF and LoT, but uses a file with extension .ldf. The boxes were defined using mdframed:
\documentclass{book}
\usepackage{xcolor}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{chngcntr}
\usepackage{lipsum}
\newcounter{exa}[chapter]
\counterwithin{exa}{chapter}
\makeatletter
\newcommand\listdefinitionname{List of Definitions}
\newcommand\listofdefinitions{%
\if@twocolumn
\@restonecoltrue\onecolumn
\else
\@restonecolfalse
\fi
\chapter*{\listdefinitionname}%
\@mkboth{\MakeUppercase\listdefinitionname}%
{\MakeUppercase\listdefinitionname}%
\@starttoc{ldf}%
\if@restonecol\twocolumn\fi
}
\makeatother
\mdfdefinestyle{mystyle}{%
linecolor=green!40!black,
outerlinewidth=1pt,%
frametitlerule=true,
frametitlefont=\sffamily\bfseries\color{white},%
frametitlerulewidth=1pt,frametitlerulecolor=green!40!black,%
frametitlebackgroundcolor=green!40!black,
backgroundcolor=green!5,
innertopmargin=\topskip,
roundcorner=5pt
}
\newmdenv[style=mystyle]{exa}
\newenvironment{example}[1]
{\stepcounter{exa}%
\addcontentsline{ldf}{figure}{#1}%
\begin{exa}[frametitle=Definition~\theexa: #1]}
{\end{exa}}
\begin{document}
\listofdefinitions
\chapter{Test Chapter}
\begin{example}{The Title}
\lipsum[1]
\end{example}\par\bigskip
\begin{example}{Another Title}
\lipsum[1]
\end{example}
\end{document}
An image of the new list of definitions:

An image of the look of the framed definitions:

The style and settings can be reused to define similar environments and lists:
\documentclass{book}
\usepackage{xcolor}
\usepackage[framemethod=tikz]{mdframed}
\usepackage{chngcntr}
\usepackage{lipsum}
\newcounter{exa}[chapter]
\newcounter{defi}[chapter]
\counterwithin{exa}{chapter}
\counterwithin{defi}{chapter}
\makeatletter
\newcommand\listdefinitionname{List of Definitions}
\newcommand\listofdefinitions{%
\if@twocolumn
\@restonecoltrue\onecolumn
\else
\@restonecolfalse
\fi
\chapter*{\listdefinitionname}%
\@mkboth{\MakeUppercase\listdefinitionname}%
{\MakeUppercase\listdefinitionname}%
\@starttoc{ldf}%
\if@restonecol\twocolumn\fi
}
\newcommand\listexamplename{List of Definitions}
\newcommand\listofexamples{%
\if@twocolumn
\@restonecoltrue\onecolumn
\else
\@restonecolfalse
\fi
\chapter*{\listexamplename}%
\@mkboth{\MakeUppercase\listexamplename}%
{\MakeUppercase\listexamplename}%
\@starttoc{lex}%
\if@restonecol\twocolumn\fi
}
\makeatother
\mdfdefinestyle{mystyle}{%
linecolor=green!40!black,
outerlinewidth=1pt,%
frametitlerule=true,
frametitlefont=\sffamily\bfseries\color{white},%
frametitlerulewidth=1pt,frametitlerulecolor=green!40!black,%
frametitlebackgroundcolor=green!40!black,
backgroundcolor=green!5,
innertopmargin=\topskip,
roundcorner=5pt
}
\newmdenv[style=mystyle]{exa}
\newmdenv[style=mystyle]{defi}
\newenvironment{example}[1]
{\stepcounter{exa}%
\addcontentsline{lex}{figure}{#1}%
\begin{exa}[frametitle=Example~\theexa: #1]}
{\end{exa}}
\newenvironment{definition}[1]
{\stepcounter{defi}%
\addcontentsline{ldf}{figure}{#1}%
\begin{defi}[frametitle=Example~\thedefi: #1]}
{\end{defi}}
\begin{document}
\listofdefinitions
\listofexamples
\chapter{Test Chapter}
\begin{example}{The title of an example}
\lipsum[1]
\end{example}\par\bigskip
\begin{definition}{The title of a definition}
\lipsum[1]
\end{definition}
\end{document}