biblatex's default bibliography heading uses \section*{<title>} to typeset the bibliography heading in article-like classes.
The redefinition
\renewcommand{\section}[1]{%
\bigskip%
{\LARGE\MakeUppercase{#1}}\\[-1ex]%
\linia\medskip
}
disables the starred version of \section and thus causes undesirable output.
Either provide a definition that can deal with \section{<title>} and the starred version \section*{<title>} or tell biblatex to use another heading (e.g. \section). The latter can be done in many ways, one would be
\documentclass{article}
\usepackage[utf8]{inputenc}
\newcommand{\linia}{\rule{\linewidth}{0.5pt}}
\renewcommand{\section}[1]{%
\bigskip%
{\LARGE\MakeUppercase{#1}}\[-1ex]%
\linia\medskip
}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\nocite{sigfridsson}
\printbibliography[heading=bibnumbered]
\end{document}
One way to define starred and unstarred versions of your section command that do the same would be to go with (see Defining starred versions of commands (* macro) for more options, especially the xparse/expl3 option if you are using a modern TeX system)
\documentclass{article}
\usepackage[utf8]{inputenc}
\newcommand{\linia}{\rule{\linewidth}{0.5pt}}
\makeatletter
\renewcommand{\section}{@ifstar@section@section}
\newcommand{@section}[1]{%
\bigskip%
{\LARGE\MakeUppercase{#1}}\[-1ex]%
\linia\medskip
}
\makeatother
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}