I am facing a problem. I am not getting the snippet which YOAST plugin showed me. The snippet in Google search is different from what YOAST is showing. Check out the screenshots (http://imgur.com/a/ko5lQ). Let me know what is the solution of it?
It is suppose to work this way. Joost's plugin only gives you a great tool for you to optimize your snippet.
If you haven't done any optimizations whatsoever, like creating an awesome brief description of what your content is all about, Google will probably try to figure out what's the best bit of content by their own.
Just a minor edit, Google just released a video exactly replying your question: http://support.google.com/webmasters/bin/answer.py?hl=en&answer=35624
I would advise signing up for Google Webmaster Tools if you haven't already (easy to verify ownership of site with Yoast's plugin). They offer advice on topics like this and recommend NOT repeating the same meta description for every page. Google always reserves the right to change the snippet depending on your page or the keyword phrase being searched.