Your Joomla!® Tags component can be found inside your Joomla Administrator area under the Administrator menu Components tab.
When you create a new article, or open an existing Article (for example for editing), you will see on the right hand side a "Tags" label and a text box.
Inside that text box you can add your own Tags, perhaps that relate to key words inside that article.
These tags will then appear at the top of your article when viewed from your website front-end.
When you, or your site visitor clicks on a Tag a list will appear containing all articles that you have added that Tag to.
These tags also get populated inside the Tags component, allowing you to also create a Menu item titled perhaps something like "Tags".
When a visitor selects that menu item ALL tags will appear in a list, again when a tag in that list is clicked a list of articles containing that Tag is now listed allowing visitors to select an article based on the Tag that they have selected.
As an example, UsingJoomla.com has added three tags to this article:
You will see these Tags at the top of this article - click on a Tag - you will be taken to a page with "Tags", click Tags, and you will see a list albeit only one article (this one!).
Open another article and clicking a "Tag" at the top of that article will give you a list of all articles that have had that specific tag associated with it.
Putting it another way - when you click a Tag - you will be taken, in our set up here on UsingJoomla.com, to the "Tags" menu item that lists the articles containing that Tag.
Also, if you select the "Tags" menu item, you will see all three Tags - clicking any one of them (in this case) will give you a single Tags list - clicking this tag will bring you to this article.