Composer is a dependency manger. Almost every application depends on some 3rd party libraries, so instead of packing them with IU we let composer manage dependencies (download and install them). There are multiple benefits of using package manager, such as smaller project size for distribution and ability to safely and automatically upgrade any of the 3rd party libraries if any of them gets an update.
composer install in the project folder you’ll let composer read dependencies from the composer.json file and download all of them in the
vendor subfolder within your project folder. You can then use FTP to transfer all project files (including dependencies - vendor folder) to your web server.
Alternatively, if you have SSH access to your web server, you can install composer on the web server and run
composer install in the project folder on the server, saving yourself a lot of bandwidth because your web server would then download dependencies instead of yourself (on your computer; and then manually transfer them to the web server).
Take a look at this (important part starts at 05:50):