Section Heading Centering problem

If you want to centre your titles and make them blue, then redefine the title format using a package like titlesec. If all your sections and subsections are going to be unnumbered, redefine them that way, also with titlesec. If you don't want numbers in your table of contents, set the secnumdepth to 0. Here's an example:

\documentclass{article}
\usepackage{xcolor}
\usepackage{titlesec}
\titleformat{\section}[block]{\color{blue}\Large\bfseries\filcenter}{}{1em}{}
\titleformat{\subsection}[hang]{\bfseries}{}{1em}{}
\setcounter{secnumdepth}{0}
\begin{document}
\tableofcontents
    \section{Ukaaranta}
    \subsection{Shabhu Harivat}
    \section{Krostru Shabda}
\end{document}

(You can adjust the vertical spacing of the titles also with titlesec using the \titlespacing command.)

\begin{center} ... \end{center} creates a list with centered items. It should not be used for headings.

\centering works here, because you use \section* which doesn't process the argument for TOC or page headers. Your code could be changed to:

\section*{\centering\textcolor{blue}{Ukaaranta }}
\subsection*{Shabhu Harivat}
\addcontentsline{toc}{subsection}{shambhu harivat} 
\section*{\centering\textcolor{blue}{Krostru Shabda}}

For a consistent document you should create macros for the style, such as

\newcommand*{\sectioncolor}{blue}
\newcommand*{\sectionformat}{\centering\color{\sectioncolor}}
...
\section*{\sectionformat Ukaaranta}

This way you could change the style of the whole document at just one place.

For more possibilities have a look at the titlesec package which provides many features for customizing style and spacing of headings.

Add the following to your preamble:

\usepackage{sectsty}
\sectionfont{\centering}

(Source)