It might be helpful when you don't need output, example with ls command:
ls > /dev/null 2>&1 &
To execute that command in the background you're missing an & at the end. Or the name of the submission is wrong and you wanted to execute it while suppressing any output.
thanks @mhitza, fixed!
It's also useful while working with cron.
Sometimes its nice to do it without the stderr redirection (the 2>&1 part) and still see problems while its running. Even if its forked stderr will show in your shell. Same for cron, you wont loose those messages (will be in log).
If you combine it with nohup or screen, you can even log out without the program being terminated.