Claiming Google Authorship is important because it adds you as an author to your blog/website and also shows an avatar of you on the Google search results for your blog/website.
There are many articles on claiming authorship, but none of them is easy to understand, especially for new bloggers, so I will explain it here in easy way.
Step 1: Create a Google Plus profile. If you have a Google account you could easily make one easily by going here.
Step 2: Link Your website to your Google Plus profile.
To do it add this code to your website/blog between