Tags are keywords that characterise the references. Some tags are automatically downloaded with the references, but you can also add tags manually. These tags can be used for topics, of course, but you can also use "workflow tags" (to-read, to-assess), methodology tags, evaluation tags ("seminal", for example). You can tag references, but also attached files or notes.
It is not recommended to keep the tags that are automatically downloaded. Each source has its own keyword system, so there will not be any logic to your tags. To disable the automatic download of tags, go to the Settings menu -> General -> Miscellaneous and uncheck "Automatically tag items with keywords and subject headings". You can delete all these automatic tags by clicking on the 
button next to "Filter Tags" and selecting "Delete Automatic Tags in This Library".
To apply a tag to several references at once, select them and drag them onto the desired tag at the bottom of the left pane.
If some tags are particularly useful to you (especially the workflow tags or the evaluation tags), you can assign colours to them (by right-clicking on the tag and selecting Assign Color) and a small coloured circle will help you to identify the references with these tags. There are nine different colours, so you can use this function for nine tags.
The main advantages of tags: they are more flexible and can probably adapt more easily to the changes in a field of research (or in the way researchers view their field of research) over the years. They are also portable when a reference is copied from a personal library to a group library. You can also combine tags to create sophisticated search queries within your library.
Tags can be words, of course, but they can also be emoji. Emoji tags can be a great way to manage your workflow, to indicate your favourite readings (
or 
) or documents you have not read yet (like 
). You will need to assign colours to these tags in order for them to appear in your library pane.
Zotero Actions & Tags is a plugin that helps you better manage your tags, with batch processing and the ability to define custom rules. For example, automatically add an /unread tag to all new items, and remove it when you open or close the item. See the readme file for full technical details. Want to rate your items with one, two or three stars? You have the explanation too.
To install it, download the file (with an xpi. extension) to your computer, then go to the Tools -> Plugins menu, click on the gear on the right, select Install Plugin from File and select the file.