Wordpress Statistics
The Wordpress user interface allows the website owner to see who has visited their website and where they are from and what pages they viewed.
Unless you are a business this reporting system is all you need to determine how your website is performing. You can use tools such as Google Analytics with wordpress.com but in my opinion this is not necessary.
You will also see advertisments for SEO services and other "possible" ways of driving visits and income to your site.

These will cost extra!
Ads on Tumblr and other "free" Wordpress websites

Subimitting Forms - and the "Like" concept
If a Form is submitted, a contact or other form such as Booking or interest form, the form submission will be recorded in the feedback log. I think this is similar to the "Like" button on Facebook.
A Facebook user who is also is the admin for a Wordpress website in likely to be monitoring their Statistics. They are also likely to be using the Android Jetpack App on their Android phone.
However, the Jetpack App may suppress these accesses in a similar manner that forms do not send emails when submitted using a TOR connection.