Force LaTeX image to appear in the section in which it's declared

Try \begin{figure}[!htb]. In nearly all cases it helps.

Explanation of the figure placement parameters:

• h - Place figure here, if possible
• t - Place figure at the top of a page
• b - Place figure at the bottom of a page and
• ! - Over-ride default LaTeX figure placement (do not use the parameter values).

If that doesn't work then use:

\usepackage[section]{placeins}

This prevents placing floats before a section.

As Werner commented: the section Moving tables and figures in LaTeX at tex.ac.uk states:

Even if you use the placement specifier [h] (for ‘here’), the figure or table will not be printed ‘here’ if doing so would break the rules; the rules themselves are pretty simple, and are given on page 198, section C.9 of the LaTeX manual.

Use the float package with the [H] specifier. If you comment out the \usepackage{float}, the following MWE results in the figure on the second page, but as is the figure appears between the two paragraphs.

\documentclass{article}
\usepackage{float}% If comment this, figure moves to Page 2
\usepackage{lipsum}
\usepackage[demo]{graphicx}

\begin{document}
\lipsum[1]
\begin{figure}[H]
  \centering
  \includegraphics{foo}
  \caption{caption text}
  \label{fig:nonfloat}
\end{figure}
\lipsum[2]
\end{document}

You should also be using \centering instead of \begin{center}...\end{center} as per should i use center or centering for figures for more details.

If you don't want your figure to float, don't use a floating environment; you can use, for example, a center environment and (if a caption is needed) the \captionof command provided by the capt-of (or caption) package:

\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{capt-of}
\usepackage{lipsum}% just to generate text for the example

\begin{document}
\lipsum[1]
\begin{center}
  \includegraphics{foo}
  \captionof{figure}{A non floating figure}
  \label{fig:test}
\end{center}

\lipsum[2]
\end{document}

If you want the figure to float, but not passing a \section command. you can use the placeins package and its \FloatBarrier command beyond which floats may not pass. A package option allows you to declare that floats may not pass a \section command, but you can place \FloatBarriers wherever you choose.