Advantage No.1: Statistics: It tells you how much your blog is visited and from where. This is in particular useful to guage two things. One the amount of revenue your site can get, two to see viability of the website. By viability, I mean, to see how much are you getting in return for your investment (here time) which helps you to prioritize your activites on the website.
No.2: Targetting: Analytics helps you to esitmate your efforts in one goal your have set for yourself. It may be your reach in a particular region (geographicaly or by subject) or your returns from a region. It tells you what you have achieved for that period.
No.3: Search & Keywords preformance: It helps us to learn how our keywords are performing on search and how search is helping you reach to your end user. You can find out the keywords that are relevant and start using them more often knowing that you are getting good hits via those keywords. Also, it helps us analyze which keywords are not performing optimal to your expectations and work towards it.
No.4: Platform, Connectivity: For most bloggers, it wont make a big impact but other wise for a website it does. For example, if you want to check what % of users use Flash on their browsers. This helps you decide whether you want to create a flash based intro or a flash based application for creating a dynamic application. The same stands true for Operating systems, but it is not that important these days as most advance browsers behave almost same in terms of delivering your content. However, your Operating systes are important to know when you want to check Mobile OS. Which helps you to categorize and calculate your visitors from Mobile Browsers. Opera on PC/Mac can be confused with Opera on mobile and hence this parameter helps.
Knowing Connectivity is important as well, to gauge what size of webpage your users will be able to download fast. If you have more thna 50% of users on dailup with 28KBPS speed, it wont help having a website that is heavily loaded with graphics.
All in all, analytics is used to target your website to a sect of users with importance to multiple aspects and you working towards achieving your targets.