Tags are like key words, but significantly different....
traditional key key words on the internet were set by the page / site coder, and eventually by content authors where platforms allowed them to do so. In forums, contributors could not set keywords. In such environments keywords tended to be set on a site wide, or at least application wide basis. The same is true for many blog applications, especially if you do not own the blog site, like tumblr or the WordPress site.
What Mike says regarding search engines is accurate.
Keywords are still used. They are included in search and ranking algorithms but they are subject to abuse and used as part of search engine spamming techniques. This is why sites like Tumblr and WordPress did not open up keywords to blog authors, unless they ran WordPress on their own domain and server (no sense in tainting their own domain and server)
The most appreciable difference between tags and key words are that tags are publicly visible, key words are not.
For this reason, tags have become part of the navigation sites, often via the concept of a "tag cloud". The concept is simple. When someone arrives at a site, a view of the tag cloud is displayed on the site. This is a randomly spaced collection of tags, where the size, boldness, and sometimes the font are varied according to tag popularity. The bigger and bolder, the more popular the tag. For example if tag1 is used 20 times, and tag2 40 times, in the tag cloud tag2 will be a larger font and bolder font.
Tag clouds are also clickable, generally taking you to a list of posts using that tag, often ordered by date or popularity.
Tags also allow you to see what a topic is about without going and reading the whole topic. When Songstuff is busier this could be very useful.
Tags are also related to, but not the same as hashtags... though for convenience and uniformity it can be wise to include a hashtag as a tag.
Hashtags are are publicly displayed within topics. On many platforms they are clickable and will display a recent posts or popular posts list of entries displaying that hashtag. Importantly, hashtags have no spaces, for example #ilovesongwriting
Hashtags are popular with microblog platforms like twitter.
When writing a forum post it is a good idea to include tags. If you choose a hashtag too, remember to include it within the body of your post, and encourage people to use it if they tweet about your post... it is quite suited to promo purposes.
One important aspect of hashtags and tags is their ability to visibly display trends. That can be very useful if you are trying to be on trend, topical and measure the success of your posts, to take part in trending topics and leverage off that popularity. Artists, celebrities and businesses, even politicians use them in this way. To associate what they are talking or singing about with an event (good or bad), and is especially used in cause based promotion. So for example, if you are releasing a song where you are donating money to Help For Heroes, then including the hashtag #helpforheroes in your posts and tweets is a good idea, especially near the beginning. Including the tag "help for heroes" would also be suggested.
I don't think tags and hashtags are just for promo. Far from it. They are for improved awareness, and most topic writers, blogger, poster, wants better awareness of their content, so that those interested In a topic will take part.
I hope this helps.
Cheers
John