A tag is a very basic form of classification, consisting usually of one or two words that describe a particular piece of data. Whether that data is a photograph or a blog entry, it doesn't really matter. By tagging you have applied a very basic and lose form of categorization.
This categorization or grouping can then help others find other related items if they want to explore further. For example, this entry here has been tagged with a number of tags that you can see at the bottom of this page. But what happens if you click on one? If you click on say, "blog help" you will be taken to a page that lists all the other blog entries that have also been tagged with this. This helps your readers to 'surf' in the traditional web sense around all your content finding relevant content.
So tagging within your own blog while powerful and useful, becomes an even greater tool when your tags are used by others outside of your blog. When you publish an entry, and the web pings go out, various search engines and aggregators come and read your content. Included in this content are the tags for each entry. Services such as Technorati provide a huge window into the blogging world by primarily offering tag based browsing. Blog-City offers a window into the most popular tagged entries through their community pages.
You can quickly see what the most popular tags are. In other words, what common subjects are people blogging about. By tagging your content, you are contributing to this larger picture, enabling people to easily find your entries by very nature of association.
Tagging can be a very useful tool to help both your current readers and to help attract new readers to your blog. Be careful to tag using relevant words and don't go too deep, or use too many. Take a look at the aggregators such as Technorati or Blog-City and see how others are tagging, and what type of words they are using.
Tagging is quick, easy and most of all, painless.

What would be REALLY helpful is if BC could provide a gutter applet that
displayed the most common tags from my blog (EG My Top 10 Tags), or the
most common tags from BC.
We actually do this already if you opt to have a custom-home page. See http://compiledby.spikesource.com<
/a> for an example of how thats used.
This will be integrated into the main portlets very soon as we are moving
everything towards this much improved drag'n'drop interface. Keep an eye
out next week for a major announcement and feature addition to your blog.
www.zoundry.com offers a free blog writingeditor which is a PC client. IMHO
it's much better than bloggers own editor. It allows you to select from the
tags you've placed on previous posts.
is tagging a premium user only feature?
At the moment for main blog-entries, yes it is a premium only feature.
However, you can still tag your LinkBlog entries, they are free for all our
bloggers.
Just to complete this thread, tagging is available to ALL our bloggers on
Blog-City.