There are a handful of tagging plugins for wordpress that let you associate keywords (aka "tags") to your posts for indexing.
For the uninitiated, when you write a post using one of these tagging plugins, a new field appears in the editor that lets you specify tags that classify your post. These tags are gathered by other sites, like Technorati, and let you see all posts people have written that use the same tag.
So why is tagging different from using categories?
Some people would say it isn't any different, and I would say that they're outright wrong. But I say that because of how I segregate tags and categories mentally.
For instance, say I'm talking about a particular clothing designer on my blog, such as Donatella Versace. I may have a post about a party that I went to at which I met her, and that could be categorized under "Designers". But I may have bought a new outfit from her brand, and that would be filed in the category "Clothing". Both posts would be tagged "Donatella Versace".
If I want to read posts about clothing, I choose the "Clothing" category. Likewise with "Designers". If I want any post that had to do with Donatella Versace, I can find those posts in her tag without creating a whole category just for her. That's the first advantage of using tags and categories - The organization of my site is controlled by categories not by tags.
Maybe it's a trivial thing, but to me it's important. I don't want a heatmap of tags on my site, or if I did, I wouldn't want it exclusively in place of a category listing. You could make the same argument on search engines versus directories. Search engines are going to uncover every minute detail with no human filtering and possibly no common thread between the results. Directories will return only human-filtered results, but might not contain every site in their listings.
Tagging gives you topical search capabilities for your site that are a middle ground between categories and all-out search, but it shouldn't replace categories entirely.
The argument you often hear against tags in my example is that you could also create a category "Donatella Versace" in which to place posts about her. But what I'm saying is that screws up my organization of these topics. My site is about aspects of fashion, of which Versace may be a significant part, but she is simply one designer of many.
Imagine that I write about meeting an unknown designer. Should I create a whole category for him even though I might write one post? Wouldn't it be better to simply categorize the post into "Designers" and then tag the post "Billy Joe Bob James"? I think so.
Can you imagine having to sift through your list of 100 or more designers to find the name of that guy you met and wrote that one post about? And then can you imagine doing that with each person you met and wrote about in a single post? That sounds tedious.
It's too easy these days to add new categories to WordPress. Not that I dislike the feature, just that I think people will have to be careful how they use categories. People have asked me why I don't use WordPress categories to do "tagging", and I hope I have explained my reasoning more clearly here.
Yet this is only my take on it. You could create a blog that uses only tags via a tagging plugin, and assign every post to a single category. As long as your output displays only the tags and not the categories, it would still work the same way. The only difference is that you're not going to get the heirarchical organization of categories. If that doesn't bother you (and that's perfectly reasonable) then go for it.
I don't know if I see a way to use only categories unless you were going to forego many of the benefits of keyword tagging. It doesn't seem beneficial. Still, if you didn't let your category list get too wild, that might work for you. And of course, if you didn't care about tagging at all, then this whole discourse is irrelevant.
As an aside to this - It might be interesting to associate tags to the categories for a post. So for example, if I had assigned a post to two categories, say "Designers" and "Events", I could add "Donatella Versace" as a tag under the "Designers" assignment, and "Vienna, 13th, Life Ball" as tags under "Events". That would be cool.
