Cloning is a backup strategy that lets you make a complete copy of your hard drive to another hard drive. In OS 9, you could do that by drag-and-drop but it is not possible in OS X because there are too many hidden files that need to be copied. I have the luxury of being able to install extra drives in my Mac Pro but you can use an external hard drive connected via either Firewire or USB.
You can actually boot the computer from a cloned drive and use it as if it were your internal drive. I have Disk Warrior installed on my main drive and, of course, it got cloned to the other drive. When I want to use it on the main drive, I can insert the DW CD and wait about 10 minutes to have it boot the computer, or I can boot from the clone in 40 seconds. If my main drive crashes, I can boot from the clone and still use the computer.
My cloning app of choice is
SuperDuper but another good option is
Carbon Copy Cloner. The initial clone (copying the entire drive) can take 45 minutes or longer but SD allows you to make incremental clones (copying only those files that have changed since the last clone). This takes a fraction of the time (in my case, about 10 minutes). I run SD once a week or so. FYI, you'll have to buy a license in order to unlock SD's incremental cloning capability. If you don't pay the fee, you can still use it to make complete clones but you'll have to erase the drive each time and start from scratch. I can't comment about CCC because I haven't used it in years, but SD's interface is very friendly.
Time Machine is an Apple program that is built into the OS. For complete information, read
Mac 101: Time Machine. You cannot boot the computer from a Time Machine backup but you can revert to previous versions of files (and TM makes them automatically). Clones are one-trick ponies in that regard; they only have the files from your most recent clones. If I need, for example, a file that I made a month ago (and I had since deleted it), I can get it from my Time Machine backup but not from the clone that I just made. The nice thing about TM is that you don't have to do anything after it's set up; it does it all for you. One of my internal drives is dedicated to TM.
