The Media Library is a section in the Administration area of the WordPress website. It contains all the media files such as images and videos that you have uploaded. You can add files, edit files, view files and delete files here.
You can view a thumbnail of the image, person who uploaded the file, page/post it is associated with, number of related comments and date when it was uploaded. You can associate a title, alternate text, caption, and description to the media file uploaded.
Once the files are in place, they can be used on the front end to add to posts, pages etc. The following screenshot shows an example of the media library.
You can also download all the files in the media library using FTP protocol for backup. Alternatively, your web hosting provider will have the automatic backup solution (for example, SiteGround support auto backup) which regularly backups all the media files under the /wp-contents/uploads directory of WordPress.
There are many plugins available to enable additional functions such as increasing the upload file size limit, deletion of redundant images, folder management for images, creating categories of files etc.
When it comes to the media library, you have to reduce the size of the uploaded images and hence it is good to use a plugin like WP Smushit, EWWW Optimizer to automatically reduce the image size upon upload.
I use the EWWW optimizer, this plugin automatically optimizes the image size and also, you can optimize the existing or already uploaded older images using the bulk optimize option.