Backing Up Locally

The term local backup refers to copying your important data to devices directly connected to your computer. 

There are many different kinds of devices that can be used for local backups, but the most popular device is an external USB hard drives (or flash drives for smaller amounts of data)

Backing Up to an External Hard Drive
To back up your data to an external hard drive, connect the USB cable from your hard drive to your computer, and connect the external power supply to your external hard drive if it has one. Your computer should find your hard drive automatically, and install necessary drivers. After it is connected, your hard drive should appear either as an icon on your desktop (for Macs), or as a drive in the My Computer window (for PCs). Both operating systems offer automated solutions for backing up data.

Time Machine on the Mac:

Windows Backup for PC:
To restore files use the Time Machine or Windows back up interface. 

The disadvantage to a local back up is that it is easily lost, stolen, or damaged by fire, flood, etc.