How Google's changes affect your blog's content requirements
The idea behind both of these updates is simply to increase the quality of the search results that Google users get and, if you address them from that angle, it's not hard to understand what you'll likely need to do to promote your site successfully.
Penguin
Penguin, for having such a cute name, is actually a pretty aggressive update. This particular update is directed at web spam. If you're affected by this update, your site is probably using blackhat SEO techniques and, because of that, Google does not want it in its indexes as a relevant search result. In fact, if you're using blackhat SEO techniques, Google may well be right in its assessment of your site!
If you've made mistakes that put you on the wrong side of SEO, you can take actions to get rid of the penalties that Penguin may have hit you with already. First, try to get rid of any low-quality backlinks that lead to your site where possible. Any backlinking you paid for from low-quality sites is more of a liability than ever, so try to get rid of these inbound links if you can.
Panda
Panda is designed to increase the quality of Google search results by demoting sites that have low-quality content. These sites include content farms, which are designed as sites where huge numbers of articles are posted and links to sites looking to increase their search engine visibility.
Panda is based on researching how humans determine whether or not a site is high quality. The algorithm has the ability to "learn" these patterns and to apply them to websites. When it sees the hallmarks of low-quality websites, it demotes those sites in its rankings.
If you're using WordPress as a CMS or blogging tool, Wordpress Themes sometimes have tools that you can use to control spam on your site and to attend to the other tasks that will become more vital to SEO as Google continues to improve the quality of its filters. Make sure that your content is of a high quality and that your site is properly coded, and you should see benefits. Post low-quality content or engage in blackhat SEO and you'll likely be penalised quickly.