Display the definition of each items in beamer one by one using onslide or any method

You can use \only<overlay specification>:

\documentclass{beamer}
\usetheme{CambridgeUS}
\setbeamertemplate{items}[ball]
\usefonttheme[onlylarge]{structurebold}
\usecolortheme[RGB={205,173,0}]{structure}
\setbeamerfont*{frametitle}{size=\normalsize,series=\bfseries}
\useoutertheme{infolines}

%Packages
\usepackage{xcolor}
\usepackage{graphics}

\mode<presentation>{}

\begin{document}
    \begin{frame}{Motivation}
    \begin{itemize}[<+->]
        \item Travel time
        \item Residence time
        \item Biology
    \end{itemize}

    \begin{block}{Definition}
        \only<1>{Travel time is the time required by the particle to move from one point to another point.}
        \only<2>{Residence time is the time required for the particle to get out of the system.}
        \only<3>{Biology is the study of living things.}
    \end{block}

\end{frame}
\end{document}

Change to \only<1->, \only<2->,... if you want the description to appear cumulatively.

You could just wrap the entries within your Definition block in an itemize the same way you did for the regular itemize entries frame. That would "bullet" the definition list, but might be what you're after:

\documentclass[mathserif]{beamer} % http://ctan.org/pkg/beamer

% Setup appearance:

\usetheme{CambridgeUS}
\setbeamertemplate{items}[ball]
\usefonttheme[onlylarge]{structurebold}
\usecolortheme[RGB={205,173,0}]{structure} 
\setbeamerfont*{frametitle}{size=\normalsize,series=\bfseries}
\useoutertheme{infolines} 

\mode<presentation>{}

\begin{document}
\begin{frame}{Motivation}
  \begin{itemize}
    \item<1-> Travel time 
    \item<2-> Residence time
    \item<3-> Biology
  \end{itemize}

  \begin{block}{Definition}
    \begin{itemize}
      \item<1-> Travel time is the time required by the particle to move from one point to another point.
      \item<2-> Residence time is the time required for the particle to get out of the system.
      \item<3-> Biology is the study of living things.
    \end{itemize}
  \end{block} 
\end{frame}
\end{document}

The above avoids a vertical skipping across frames due to different text lengths in your Definition block.