Your blog depends upon traffic for its success. You need to monitor the traffic, to watch for problems. You use a visitor meter, to monitor the traffic numbers, and objectively watch for problems.
Most visitor meters give you a bare minimum of diagnostic information - what pages / posts were read, what URLs were they read from, and similar information is what you get. If you want to proactively watch for problems, that can cause your visitor meters to show changes in the numbers, you use the diagnostic tools in Google Webmaster Tools.
To better understand the changes, you will get more out of the diagnostic tools if you use them before the changes occur. Spend some time now, examining the various tools, before you have questions. Observe what's normal, before the changes happen.
A visitor meter shows you what is happening, as your visitors see your blog. Many of your visitors find your blog using the search engines - Google Search, and other Internet services are essential, to getting you new readers. Google Webmaster Tools shows you what is happening, as the search engines see your blog.