Backup and Sync lets you, well, backup and sync photos and files from PC folders, USB keys and SD cards to the cloud, so they're available anywhere. The original Google Drive was not so convenient, as it required you to use two separate apps for files and photos. That could affect your storage space dramatically -- if you upload images to Drive, it counts against your space, but if you upload them to Photos (using the "high," not "original" setting), it doesn't. At the same time, PC backups are now a more automated process.
Google also fully launched Drive File Stream, an app that performs roughly the same chores as Backup and Sync, but for enterprise and business users. It has more team-oriented features, like on-demand file streaming and access to Team Drives (for a comparison chart and other info, check here).
The loss of Drive on the desktop won't affect your life much, unless you really liked the old Drive logo, which has been changed to something that resembles Microsoft's OneDrive icon. Google also points out that you may soon see messages notifying you that "Drive for Mac/PC is going away," presumably to join Google Reader and others in the great App Graveyard.