A good use case is to redirect output into a file you only can modify with sudo. Trying to do it like this doesn't work:

  sudo echo "fs.inotify.max_user_watches=1000000" > /etc/sysctl.conf

as the redirection happens within the shell, thus without root permissions. However, the following does work:

  echo "fs.inotify.max_user_watches=1000000" | sudo tee /etc/sysctl.conf

as the writing is done by the elevated tee process.