What is the Webmaster tools and usage of this tools ?
They’re exactly what you might expect them to be - tools to help webmasters. 
The best way to find out about them is to sign up for an account and explore what’s available.
Webmaster tool will help us to find out website issues like crawler status,site error,fetch status also site performance.this tool give all the information.
It’s a tool that would help you diagnose any issues on your site, as mentioned by others above. Do not miss to submit your site to the webmaster tool, especially your sitemap. It helps a lot in indexing your site’s pages. I noticed a spike in our traffic ever since I submitted the site to the tool. There is a huge difference, traffic-wise, between websites submitted to the tool and those not submitted, IMO.
It is the place where you can check all about your website. like Website 404 errors, Links related to your website, Index pages, Duplicate Title tags, Duplicate meta description etc.
in my opinion you should use Google Webmaster tools
Why? What’s the benefit? Are you saying it’s the only one worth using, or what?
A sweeping statement like that isn’t much use to the OP. You need to explain the reasons behind your opinion, if you want to be really helpful.
Web master tool is a free web tool which is use for see traffic and provide whole website performance report.
As the OP has not returned with further questions, I think it’s safe to assume they’re happy with the answers already given, and close this thread.