By default, bookmarks replicate the table of contents. So if your ToC shows content up to \section, so will the bookmarks. The default level up to which content is shown in the ToC is 2 - equivalent to \subsection (in book and report). So, the following minimal example
\documentclass{book}
\usepackage{bookmark}
\begin{document}
\tableofcontents % Level 0 (chapter)
\chapter{A chapter} % Level 0
\section{A section} % Level 1
\subsection{A subsection} % Level 2
\subsubsection{A subsubsection} % Level 3
\paragraph{A paragraph} % Level 4
\subparagraph{A subparagraph} % Level 5
\end{document}
shows the bookmarks up to level 2:

If yours doesn't show up to this level, then you must be using a different class, or perhaps a package that sets a different level of inclusion. This can be changed though...
By adding
\setcounter{tocdepth}{3}% Show ToC content up to level 3 (\subsubsection)
to your preamble to ToC/bookmarks resemble

The above works the same with hyperref as it does with bookmark.
You can have different depths of visibility in the ToC and bookmarks. This is provided by the bookmarks option depth.

\documentclass{book}
\usepackage[depth=4]{bookmark}% Show up to level 4 (\paragraph) in bookmarks
\setcounter{tocdepth}{3}% Show up to level 3 (\subsubsection) in ToC
\begin{document}
\tableofcontents % Level 0 (chapter)
\chapter{A chapter} % Level 0
\section{A section} % Level 1
\subsection{A subsection} % Level 2
\subsubsection{A subsubsection} % Level 3
\paragraph{A paragraph} % Level 4
\subparagraph{A subparagraph} % Level 5
\end{document}
\usepackage{hyperref}– Henri Menke Dec 30 '16 at 20:32\usepackage{bookmark}will also be helpful... – Dec 30 '16 at 20:32\usepackage[depth=subsection]{bookmark}will show the subsection bookmarks, thebookmarkpackage 'translates' the relevant section level into the level number (which is 2 for subsection, sodepth=2would work too) – Dec 30 '16 at 20:49