The meta keywords tag allows you to provide additional text for crawler-based search engines to index along with your body copy. How does this help you? Well, for most major crawlers, it doesn't. That's because most crawlers now ignore the tag.
The meta keywords tag is sometimes useful as a way to reinforce the terms you think a page is important for the few crawlers that may support it, now or in the future. For instance, if you had a page about stamp collecting -- and you say the words stamp collecting at various places in your body copy -- then mentioning the words "stamp collecting" a few times in the meta keywords tag might help boost your page a bit higher for those words.
Remember, if you don't use the words "stamp collecting" on the page at all, then just adding them to the meta keywords tag is extremely unlikely to help the page rank well for the term. The text in the meta keywords tag, for the few crawlers that support it, works in conjunction with the text in your body copy.
The meta keyword tag is also sometimes useful as a way to help your page come up for synonyms or unusual words that don't appear on the page itself. For instance, let's say you had a page all about the "Penny Black" stamp. You never actually say the word "collecting" on this page. By having the word in your meta keywords tag, you may help increase the odds of coming up if someone searched for "penny black stamp collecting." Of course,you would greatly increase the odds, if you just used the word "collecting" in the body copy of the page itself.
Here's another example. Let's say you have a page about horseback riding, and you've written your page using "horseback" as a single word. You realize that some people may instead search for "horse back riding," with "horse back" in their queries being two separate words. If you listed these words separately in your meta keywords tag, then, maybe for the few crawlers that support it, your page might rank better for "horse back" riding. Sadly, the best way to ensure this happening would be to write your pages using both "horseback riding" and "horse back riding" in the text -- or perhaps on some of your pages, using the single-word version on some pages and the twoword version on others.
I'm emphasizing various phrases in this article on purpose. Far too many people new to search engine optimization obsess with the meta keywords tag. Few crawlers support it. For those that do, it might! maybe! perhaps! possibly! but with no guarantee! help improve the ranking of your page. It also may very well do nothing for your page at all. In fact, repeat a particular word too often in a meta keywords tag and you could actually harm your page's chances of ranking well. Because of this, I strongly suggest that those new to search engine optimization not worry about the tag at all.
Even those who are experienced in search engine optimization may decide it is no longer worth using this tag. Search Engine Watch doesn't. Any meta keywords tags you find in the site were written in the past, when the keywords tag was more important. There's no harm in leaving up existing tags you may have written, but going forward, writing new tags probably isn't worth the trouble.
Hopefully that will help you out