What do we mean by file or folder synchronisation? Well let's suppose you are worried that your My Documents folder on your C:. You want to copy it to your USB flash drive for safe keeping (to make a 'backup' of it). In Windows Explorer you could copy/paste My Documents to the USB flash drive. That would work fine. However, let's say tomorrow, you change one or two files in My Documents on your C:. Using Windows Explorer you'd have to copy/paste the entire My Documents all over again. But what if you could copy just the files that were new or changed? That is synchronisation, where a software program looks at folders in two locations and compares them. It makes them identical.
Synchronisation can save a lot of time because it only copies the difference, not all the files/folders.
There are many file synchronisation programs but I've found FreeFileSync to be very good. It's free for personal use and it's relatively simple. For more information see http://freefilesync.sourceforge.net/
If you need to backup files then you should consider cloud services such as Carbonate and also hard disks that come with specific backup software. Take a look at my previous post on the subject of backups - it might also be useful: http://mgxp.blogspot.com/2011/10/backup-your-data.html
Update January 2015
Robocopy - command line file/folder synchronisation: