I hate to assume, but I am going to have to. I assume that "they" have been referring to Time Machine, which is the native backup software on all current Macs. If so, then yes, you will want an external hard drive that is twice the size of the drive in your Mac. This is a general rule, but one to paid attention to.
On my MBP, I have a 1 TB drive hooked up to my Airport Extreme that is used only to back the computer up with Time Machine.
On my MacMini, I have a 1 TB drive hooked up directly to the machine to use with Time Machine.
The first time you connect the drive to Time Machine, it will guide you through getting it set up properly. Then, it will run a complete backup of the system to the TM drive. After that is done, TM will only backup changes to the drive; like if you install, remove, add, delete any files of applications, including photos. What is nice about this is that you can literally go back in time for previous version of individual files or full restore after installing an errant application.
It is because of the incremental backups that you want a larger drive. At a certain point, no matter how large the drive, it will have to overwrite previous incremental backups in order to keep going. This is normal. The one on my MBP took a year before it got to that point, but it is working flawlessly and maintained the very first full backup, just removing the oldest incremental. My MacMini hasnt been online that long yet, and because most of its data is on another external, it will be a while before it will start overwriting.
TM has saved my **** a couple times when I thought I lost a Final Cut Pro project. Kept us from having to reshoot.
Lots of info, yes. But it works.
Both my computers have 500GB drives, which is why I go the 1TB drives.