What is a taxonomy? A taxonomy is a way for grouping things together like in WordPress you can use a taxonomy for grouping articles from same topic together. Tags and categories are default WordPress taxonomies, there are also various plugins and hacks which enables you to register custom taxonomies as well.
By default taxonomies uses a base slug like a taxonomy with name ‘Topics’ would be looking something like this: http://yourdomain.com/topics/topic-name. Removing any taxonomy’s base slug means making it look something like this: http://yourdomain.com/topic-name.
WP No Taxonomy Base removes the base slug for both custom taxonomies and also the default WordPress like category. All you have to do is install and activate the plugin and you’re done.