HTML <meta> tags are used to provide supplemental information about the page, but not actually change the way the page is viewed in the browser. It is mainly used to denote keywords and description, but can also be used to list copyright year, author, which software was used to create it, et cetera.
Meta tags are easily abusable, so search engines don't rely on them to any great degree. There is certainly some debate about their effectiveness. But since meta tags are easy to add, and can only help and not hurt, they are generally regarded as a required element for SEO.
Keywords
Obviously, if a site could pick it's keywords so easily, every site would use every word in the dictionary and the whole thing would be useless pretty quick. Someone with a site about SEO consulting services could include "web site design, programming, advertising, marketing, free money, gold, britney spears, U.S. Election" and go on and on to areas that are totally not related to their site. So search engines do NOT generally trust a site to pick it's own keywords.
But, it can't hurt to have them. Don't put too many, and keep them closely related to the page content. For bonus points, each page should have slightly different keywords.
Description
The description given in the meta tags is actually used by Google to describe your site. It should be something written to entice a user to click on your site. Obviously, it's tempting to go to either extreme, either with a completely boring description ("A site with my thoughts on things") and one full of marketing sales junk ("I am the greatest programmer in the world, and let me share my secrets"). The best written descriptions probably entice the user to come to your site based on what you're likely actually going to provide them ("A site devoted to sharing concrete SEO tips I have learned over the years, that lead to measureable results.").
To the best of my knowledge, most search engines do not take the description into account when assigning a ranking to your web site, but it does help people get there.
Robots
A relatively new meta tag is the Robots tag. The purpose is to help search engine (and other automated web crawlers) know your site policy on indexing content. Do you even want crawlers viewing your site? If you don't, this is where you can tell them. And do you want them giving additional credibility to sites you link to (called Google Juice)? Both the indexing and link-following attributes can be set with this one tag.
In general, here are some tips for setting up meta tags:
- It's good to have them, even if their value is debatable
- Don't have too many keywords, 10 or 12 at the most
- The description is sometimes shown by search engines, so make it entice the user to click on the link
- Sites that may contain a lot of links to questionable areas of the internet (spam) should turn on the NOFOLLOW robot attribute