Quite frankly, no one really cares about search page. I too, previously, until the day I search for a site and find it hard to catch the terms on the search page. Instead of finding it, I search using browser CTRL+F again, double my search job.
There are numorous of plugins available for WordPress to highlight the search terms, some even have tutorial on how to highlight without using a plugin. I tested, it doesn’t work too well for me. Perhaps, the updated version of JQuery conflicted with it.

Yet again, WordPress template tags comes to save my time
There is this the_search_query tags in WordPress. It will shows the term you searched. Simply, .replace() it with JQuery.
<script type="text/javascript" >
jQuery(document).ready(function($){
jQuery(".post").each(function() { // The DIV of the result
jQuery(this).html(jQuery(this).html().replace(/ <?php the_search_query(); ? >/ig, " <span class='highlight' > <?php the_search_query(); ? > </span >"));
});
}); // END
</script >
Simply placed the above code in search.php and you’re good to go
