Very simply, a redirection operator can be used to redirect the output of a command (what the command displays on the screen) to a file. In other words, whatever the command was going to spit out on screen, it instead saves to a file.
If it hasn't dawned on you already, using a redirection operator can be extremely useful when running certain kinds of commands like ping, dir, systeminfo, and others that display tons of information that would be great to save and reference later.
Here's a really simple example:
ping 192.168.1.1 > c:\pingresults.txt
With the results of the ping command now saved to a file, I can email or post that file anywhere I want, providing really detailed information to someone helping me with my home networking problem. This works the same in Windows 8, Windows 7, Windows Vista, and Windows XP.
If you need some more help or want to see some more examples, check out How To Redirect Command Output to a File.