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 logs and meters give you a bare minimum of diagnostic information - what pages / posts were read, what URLs were they read from, and similar demographic information about your visitors.
If you want to proactively watch for problems, that can cause your visitor meters to show changes, you use the diagnostic tools in Webmaster Tools / Search Console.
To better understand the reports provided by Webmaster Tools / Search Console, you will get more out of them if you use them before you have questions.
Spend some time now, examining the various tools, now. 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 / Search Console shows you what is happening, as the search engines see your blog - and helps you identify problems while they can be corrected.