The words thin content comes from a warning that Google may issue to sites: "Thin content with little or no added value".
This refers to non-original or duplicate content on your site -- often the result of using syndicated content. Search engines may lower rankings or even de-index sites with a large amount of thin content on them, so it's definitely something webmasters will want to avoid.
One of the most common examples is an eCommerce website with thousands of products. Rather than writing their own descriptions for each product, they simply use the manufacturer's description that came with the product feed. The problem with this approach is that many other sites may do the same thing, thus creating large amounts of duplicate or near-duplicate content.
Besides product feeds, this can also happen when using other types of syndicated content, such as republishing RSS feeds, re-using articles from other sites on your own.
Thin content may also refer to other more nefarious techniques, such as using scraped content, doorway pages, or thin affiliate sites. It goes without saying that all of these techniques should be avoided.
Instead of re-using others' content on your site, it's always best to fill your site with good quality, original content. When it makes sense to use others' content, do so in moderation, and be sure to add value to it -- do not just copy the content straight to your site. Add your own ideas and content to augment it.