Display a separator between teasers on the front page
You might want each node (aka post) on the front page of your site to be separated from the next one, making it stand out a little from the next one. In that case, depending on the theme you're using, selecting this box will cause a small separator to be displayed between each node on the front page.
Display a separator between teasers throughout the entire site
Same as above, except the rule applies to any teasers found on your site (not just on the front page, although the front page is included if this option is selected). The above setting has no effect if this box is checked.
Display user pictures inside teasers
By default, Drupal core has never offered an option to exclude user pictures from teasers only, and it doesn't look like that will change with Drupal 8 either. It does give the option to exclude (or include) submitted by information on each content type, but there is no option for differentiating between teaser mode and full-page mode. By (de-)selecting this box, you can toggle whether your users' pictures -- if they have pictures -- will be displayed in full-page mode and in teaser mode, or just in full-page mode (not within teasers).