You can use for example the enumitem package to customize the enumerate environment.
\documentclass{article}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}[label=Property \arabic*.,leftmargin=*]
\item First
\item Second
\end{enumerate}
\end{document}
enumitem also allows you to define your own list environment:
\documentclass{article}
\usepackage{enumitem}
\newlist{Properties}{enumerate}{2}
\setlist[Properties]{label=Property \arabic*.,leftmargin=*}
\begin{document}
\begin{Properties}
\item First
\item Second
\end{Properties}
\end{document}

As commented by Gonzalo Medina, the leftmargin should be increased. The reason for this is demonstrated by the following example:
\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{enumitem}
\newlist{Properties}{enumerate}{2}
\setlist[Properties]{label=Property \arabic*.,leftmargin=*}
\begin{document}
\begin{enumerate}[label=Property \arabic*.]
\item First.
\item Second.
\end{enumerate}
\begin{Properties}
\item First.
\item Second.
\end{Properties}
\end{document}
which will show you this:

Loading geometry with showframe gives you a frame that shows the boundary of the text area, and as you can see here, unless the leftmargin is increased, "Property" will extend into the left margin of the page.