Risto Niinemets

Most commonly taxonomy sorting plugins will create a new interface to drag or order/sort your terms. This plugin uses the built-in view just to make things easier. Just grab the term and drag it to a new position. No more extra clicks – everything is saved after repositioning!

The Taxonomy Sort

I would advise against using this plugin. In the latest WordPress update, selected categories are no longer displayed on the posts page. Deactivating the plugin shows the selected categories once again. It's too bad, this was a useful tool.

Broken in WordPress 4.7

Allows you to easily change the order of different taxonomies/terms/categories.

Drew Gourley

Order Up!
A series of plugins for WordPress which allow for the ordering of pages, posts, and taxonomies through a simple 
drag-and-drop interface using the available WordPress scripts and styles. The plugins are extremely lightweight, 
without a bunch of unnecessary scripts to load into the admin. They also fall in line gracefully with the look 
and feel of the WordPress interface.

Custom Post Order

Allows for the ordering of posts and custom post types through a simple drag-and-drop interface

The Taxonomy Sort vs Custom Post Order