Analytics is basically a statistical analysis of your log files.
I believe there are two aspects of what you can do with analytics:
1. You can actually get the log files for yourself and use a log analysis from a security and performance point of view. You can check which pages are being asked, what are the queries passed etc. This way you can check whether there are any loopholes in your code, vulnerabilities, scripts that are being accessed a lot, resources that need to be cached etc. Google Analytics gives you some of that data (top queries, etc.) but not from a security perspective.
2. You can plot data over time for each website and use them for marketing purposes i.e. growth over time
I believe there are two aspects of what you can do with analytics:
1. You can actually get the log files for yourself and use a log analysis from a security and performance point of view. You can check which pages are being asked, what are the queries passed etc. This way you can check whether there are any loopholes in your code, vulnerabilities, scripts that are being accessed a lot, resources that need to be cached etc. Google Analytics gives you some of that data (top queries, etc.) but not from a security perspective.
2. You can plot data over time for each website and use them for marketing purposes i.e. growth over time
I hope the above helps.