Tree is an useful linux command to display a tree representation a full directory structure or a part of it.
On a Debian based distro like Ubuntu install:
sudo apt-get install tree
The last line of tree print a line like this:
346 directories, 174 files
If you’re changing files and directories and you want a real-time update of files and directories number, you can use watch.
watch -n 20 'tree | tail -n 1'
Tree will print the tree, tail will extract the last line, then watch will refresh the result every 20 seconds.