An inheritance group is similar to an element group by means that they allow you to drop a set of content elements into your page as a single object. But element groups don't allow you to change the set of elements only for a specific subset of pages. When you make a change to an element group, this change is visible across all pages using that element group. This is the problem that inheritance groups are meant to solve.
When changing an inheritance group on a page, the content of the same group will only be changed on the page and any pages which are descendants of the page's parent folder. In other words, changes will be "inherited" by the group in child pages, but nowhere else. For example, you may want to define an inheritance group for the right column of your template, define some common content which you want to be visible everywhere on your site, and then add more specific contents for each subsite.