In WordPress, the text domain is a unique identifier that allows WordPress to distinguish between all loaded translations. It also makes it easier for WordPress to know which strings belong to each of your themes or plugins. The text domain should always match the slug of the theme or plugin.
It’s also worth knowing that in order for a plugin or theme to be translation-ready, it has to have a text domain.
Here’s an example from the String Translation page. In Auto register strings for translation, you can enable the option to Look for strings while pages are rendered. Clicking Edit shows you all the text domains on your site and allows you to exclude specific text domains from being auto-registered: