Clicking on the Stats dropdown will display a menu where you can choose the type of chess stats you want to see:

The first thing you'll notice is a graph displaying your progress. This shows your rating changes by day over the past 7, 30, 90 a year, or all time.

Above the graph, you can see your ranking among your friends and globally.

Below the rating graph, you can view the highest rating you've achieved and the date you reached it. This will be updated each time you surpass your previous highest rating:

This section details all your wins, losses, and draws. You can toggle between white or black pieces to see your ratios for each color or search for a specific opponent to view the breakdown of games against them:

This section provides details about your average opponent, categorized by wins, losses, and draws.

In the below image, the average opponent rating is 2915 overall. When looking at only wins, the average opponent rating is 2892, for losses it is 2998, and for draws it is 2985.

You can also see your best overall win and your longest win streak listed here:

This is only for Daily Games.

This shows your average move time in Daily games, including conditional moves. Since a conditional move takes zero time to play, using them whenever possible can significantly lower your average.

Check out this article for more information on conditional moves: How do I make conditional moves?