A "short extract" refers to a small portion or a brief piece of something, like a passage from a book, a segment from a song, or a part of a conversation. It doesn't include the entire thing, only a small section. Full definition
You may remember the Belgian newspapers» lawsuit to prevent Google from linking to their sites, or from running short extracts from their sites in a Google News aggregation — a lawsuit that (if I recall correctly) the papers succeeded in, then found that they had a lot less traffic on their sites, so they made an arrangement with Google. (slaw.ca)
We are happy for students to quote short extracts of our articles for their school / college coursework, as long as New Scientist is clearly credited as the source. (newscientist.com)
The final short extract comes from a 2011 letter from Jeremy Grantham. (mastersinvest.com)