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 Preferences menu -> General and uncheck "Automatically tag items with keywords and subject headings". You can delete all these automatic tags by clicking on the little small triangle next to the coloured squares at the bottom right of the tabs pane.
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 square 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.
Zutilo and Zotero Tag are two plugins that help you manage your tags better, with batch processing and the ability to define custom rules.
To install them, download the file (with an xpi. extension) to your computer, then go to the Tools -> Add-ons menu, click on the gear on the right, select Install Add-on from File and select the file.
Zutilo allows you to copy, remove and delete sets of tags.
Zotero Tag has the same batch processing options, and it adds 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. Full technical details in the readme file. Want to rate your items with one, two or three stars? You have the explanation as well.