documentclass{article}

usepackage{amssymb}
newcommand{+}{boxplus}
renewcommand{-}{boxminus}

begin{document}
  Plus $+$ and minus $-$ work here.
  begin{figure}
    caption{Why does $-$ not work in a caption while $+$ works?}
  end{figure}
  begin{table}
    caption{Why does $-$ not work in a caption while $+$ works?}
  end{table}
end{document}