When you enter a Post in WordPress, you can also enter an excerpt to override the automatic excerpt generated by default from the first 55 words of the post. This text is displayed in post lists and grids. For instance, the general “posts” page, category lists, tag lists, date-based archive pages, and internal search results on your site.
When creating a Page (as opposed to a Post), some themes let you add an excerpt while others do not. I don’t understand why they wouldn’t enable this function. Pages can also appear in your site’s search results, and they can appear in customized page lists generated via the Query Loop block or by specialized plugins such as CC Child Pages, for instance.
In case your theme doesn’t let you set the excerpt text for pages, the Torknado Page Excerpt plugin adds that functionality. If your theme does already let you do this, the plugin does no harm (it won’t display the excerpt field twice, for instance), but in that case you don’t need it.