If you want to know how the new users during a specific period of time are interacting with your website the Cohort report in Google Analytics is a great place to begin.
Together with Segments it is one of the most powerful reports that exist in analytics when you want to study a specific portion of users. The difference between a segment and the cohort report is that the cohort lets you have a look at certain user behaviours over a period of time. The report lets you follow a crowd that visits your site for the first time during period x and let you compare it with the people who visited your website during period y.
This is especially good if you want to see how good a change to your app or website has been at explaining your service, tool, platform to new users in comparison to old users.
If you bundle them together you’ll get an average and won’t be able to look at how your changes affected the user’s experience of your product. I use this especially when I try to evaluate the stickiness of my service. If more new users come back, I know that I have explained my product in a more useful way as they know why they should use it and thus, use it more often.