I followed these instructions from Google, and my authorship came through instantly. Easily insert the code in the header tag of your website, and insert your Google+ profile in the address.
Here's why it's important:
1) Authorship gives you credibility and protects your content.
2) Google search algorithms have changed to focus more on whole pieces of content that answer questions versus key words.
3) Activity on social media tells google that you can be trusted and that you are who you say you are.
So link up, write unique content, and be social on your social media enterprises, and watch Google rank you higher in search.