When people design websites, with CSS frameworks like YAML (Yet Another Multicolumn Layout) they speak about teasers in their designs, I have no idea what do they mean.
Just a snippet of a blog post that encourages the reader to click for the whole thing.
Like this one:
agree with @rich, teaser can be used to pull out most popular discussion, comments, posts.... to inform people with what's going on. It also helps to keep visitors staying longer on a site