Backup Software (more properly backup and restore software) automates the creation, management and recovery of copies of computer files (documents, spreadsheet, video, email, etc.). Backup software has existed for many years and has evolved over that time as technologies have changed and as important records and documents are increasingly being stored exclusively electronically. Many different backup products and services exist to service home, small business, Fortune 500 companies and governments.
For more information:

• Wikipedia Introduction Site
• A summary report from Gartner 
• Connected Backup -- a product I managed