How to change style of section titles

I suggest you run either

usepackage{sectsty}
subsectionfont{mdseriesitshape}

or (as already suggested by @Bernard)

usepackage{titlesec}
titleformat*{subsection}{largeitshapemdseries

in the preamble. Note: load either titleformat or secsty, but not both.

Both methods shown above will render the subsection header text and the associated subsection number in italics. If you want the subsection number to be rendered in an upright font shape, I suggest you also include the following code in the preamble:

makeatletter % See pp. 26f. of 'The LaTeX Companion,' 2nd ed.
def@seccntformat#1{@ifundefined{#1@cntformat}%
   {csname the#1endcsnamequad}%    default appearance
   {csname #1@cntformatendcsname}}% enable individual control
newcommandsubsection@cntformat{upshapethesubsectionquad} % subsection level 
makeatother

A full MWE and its output:

documentclass{article}
usepackage{tocloft}

usepackage{sectsty}
subsectionfont{mdseriesitshape}

% See pp. 26f. of 'The LaTeX Companion,' 2nd ed. 
makeatletter
def@seccntformat#1{@ifundefined{#1@cntformat}%
   {csname the#1endcsnamequad}%    default appearance
   {csname #1@cntformatendcsname}}% enable individual control
newcommandsubsection@cntformat{upshapethesubsectionquad} % subsection level 
makeatother

begin{document}
tableofcontents

section{Section title}
Section text

subsection{Subsection title}
Subsection text
end{document}