As a SharePoint administrator, I'm totally sure you have had to answer the question about how many people are using your site and you didn't know what to say. This kind of information has been usually difficult to find and get in the past. Now, seems to be a little easier and a little prettier to get and understand the usage metrics of your site.
One thing you have to keep in mind is that you only have the information for your site - and with "site" I mean only the site (the SPWeb if you are used to developing with SharePoint Object Model) and not the site collection. If you want to have complete usage of all of your sites, and subsites and subsubsites and so on, you have to navigate through each of them and build a spreadsheet, do the proper calculations and update each time you need it.
Well, I have to say that there are not so much but enough for a basic understanding of your site users:
Unique viewers: bar chart showing the number of unique users that access any of the site pages, documents or news for the last 7 days, last 30 days and last 90 days. Besides, you can see the lifetime total unique viewers,
Site visits: bar chart showing the number of visits that access any of the site pages, documents or news for the last 7 days, last 30 days and last 90 days. Besides, you can see the lifetime total visits,
Site traffic: heat trend map that shows the visits to the site daily and hourly. The darker the box is the most visits the site received at this hour. You can show this information for the last 7 days, last 30 days and last 90 days,
Popular platforms: horizontal bar chart showing which platform is the most used by users. You can show this information for the last 7 days, last 30 days and last 90 days,
Most unique viewers: shows a list of files and pages with the most unique viewers just for the last 7 days,
Most viewed: shows a list of files and pages with the most views just for the last 7 days,
Shared with external users: shows a list of files that have been shared externally.
As I said before, this kind of information can be very basic to people that get used to working with Google Analytics or similar services or applications. But, these charts and data make an administrator able to understand how users use her site.
Let me expose here some examples of what you can know from these metrics:
Understand when users are active: Checking the "Site visits" bar chart you will see the days where people accessed your site for any reason: if you are maintaining a Newbie Employee site and your company hired several employees one week ago, you will likely be able to see an increase in the site visits for that week.
Understand when something is really interesting for each employee of the company: Let's imagine you are the administrator of the Internal Communication site and you published relevant news about the company stocks. Checking the Unique viewers chart plus the Site traffic heat map you can report if employees were interested in that news, how many of them and when. That could be important for your company to understand whether the information is relevant or not to the employees.
Understand people timelines: Let's say your site contains training information. You can determine when are the best hours for your employees to access and learn something new. The Site traffic heat map will show the time employees are ready to learn something. Going further, Popular platforms chart will tell you which device they are using to access and learn. That's a good point to understand how the material has to be prepared and be ready for. Don't forget to read the Most viewed file list to see the course that most requested for your users.
Here I exposed only three examples on how SharePoint Usage Metrics can be used but you can find your ones and extracting information to make a better site for your users.
Share with us your experience and if these metrics are useful for your purposes, write a comment with the explanation so all of us can keep growing up.
I extracted the information of this article from the View usage data for your SharePoint site Microsoft web page and my own experience. Hope this can help you in some way.