mysqli large amount of connections
1) How can it be?


If you check the documentation for server status variables, this number (3551496) is:


  The number of connection attempts (successful or not) to the MySQL
  server.


i.e. the number of connections (plus attempts to connect) since the server was booted!

The number of active connections can be verified by looking at the Threads_connected variable, which gives you:


  The number of currently open connections.


(which is at the bottom of your image and is 29!)

The show processlist command gives you more information about your active connections!

You need to make sure that you're using a privileged user:


  Like the output from the corresponding SHOW statement, the PROCESSLIST
  table will only show information about your own threads, unless you
  have the PROCESS privilege, in which case you will see information
  about other threads, too. As an anonymous user, you cannot see any
  rows at all.


You will find more relevant information here - the processlist table!


2) What should I do about it?


Congratulate yourself on a site which appears to be running nicely! :-)