Out of the box, WordPress does not support the ability to reorder posts within a term. There are other plugins out there that do term ordering, but they usually create custom tables (which require crazy custom queries and filters) and/or add a column or two to core tables, which is not sustainable in the long-term should WordPress core decide to update its schema.
Reorder by Term uses custom fields, which means you can reorder by term within each taxonomy AND post type. This is insanely flexible.
Since WordPress doesn’t support this by default, when you install the plugin, you’ll have to build the term data. For a lot of posts and terms, this can take a while, but you can limit the build to post types and taxonomies if, for example, you don’t want to touch regular blog posts (with categories and tags).