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In simple terms the answer is - many ways :)
1) It help you to give ideas about what all keywords that bring traffic to your website
2) It provides you keyword based search impressions & CTR of each keyword. It also gives the changes over month..
3) It notify you on security related information such as your codes are clear from vulnerability or not... Or it points out the recent malware that affected the search visibility of your website
3) It gives you no of backlinks to your each pages + info of those incoming links
4) It provides detected markup languges in your code. Hence you can alter the code to present your webpage in Google search better.
5) It shows you how many pages indexed in google so far and provide the chart based on months. Hence, you can note down the change in total number of indexed pages over month. This can help you to figure out how the traffic to website changed over month and its reasons...
6) It provides crawl errors, blocked URLs in robots.txt and many more
Ultimately, it notify a webmaster about website status then and there :)