Composer will create a new directory called MY_PROJECT containing a docroot directory with a full Lightning code base therein. You can then install it like you would any other Drupal site. The magic is that Composer, unlike Drush, is a dependency manager. If module foo version: 1.0.0 depends on baz version: 3.2.0, Composer will not let you update baz to 3.3.0 (or downgrade it to 3.1.0, for that matter). Drush has no concept of dependency management. If you've ever accidentally hosed a site because of dependency issues like this, you've probably already realized how valuable Composer can be.