Grav is a content management system (CMS) or, said another way, it’s an application to make websites. But differs from other CMSs like Drupal or WordPress in its underlying technology. While it’s a PHP app like those two, unlike them it does not have a database. All data is written directly to files rather than stored and retrieved from a database. This is known as a flat-file system and it can help with performance given numerous database calls can slow down sites.
Why and when would you use Grav? Grav should maybe be reserved for the technically-savvy user. It’s not that Grav is particularly difficult (every CMS has a learning curve) but rather it gets really interesting when you can integrate it into Github using the Github Sync plugin, which syncs everything on your Grav site to a Github repository for others to contribute to, clone, or fork. Grav also requires a familiarity with Markdown, a lightweight Markup language, so that’s something to be aware of as well.
You can learn more about Grav here.