Michael Tyson had a cool idea: instead of the search results page showing an excerpt of the first words of the post, show an excerpt that contains the search terms and highlight them (say, by making them bold). I thought his method was too complex—it requires replacing your theme's search.php
with a custom page, and it shows the context of every occurrence of the search terms. I thought it would be more straightforward to use the existing search page, which should be using the_excerpt
to show an extract of the found page, and use the existing filters to change the text. Also, there's no need to show every occurrence of the search terms; the first ones should be fine.