What happens when you use tags is that you create a page that is called www.your-domain.com/tag/tag-name. You also have the original blog post which is www.your-domain.com/blog-post.
They have two completely separate URLs, but they have the exact same content.
This is exacerbated when you use multiple tags because you increase the amount of chances for duplicate content to be created. And again it's even more expounded when you take into account the Categories, and Date Based Archives.
The solution is to use something like the Yoast WordPress SEO plugin and use no-index for everything that you don't want indexed. In my case I want Categories indexed, so I no-index Tags and Date Based Archives.
If you use Yoast's plugin I have put together a fairly easy article on how to initially set it up, and it is pretty helpful in understanding some of the settings. It's geared mainly for photographers running their own site, but should be just as valuable to you.
You can find it here http://www.themoderntog.com/how-to-configure-wordpress-seo-plugin-by-yoast-for-maximum-online-exposure