It's like the opposite of && (continue until one alternative is false), for if you want to continue with alternatives in sequence until one alternative becomes true: a || b || c || ...
This usage is commonly found in other places than the shell, like JavaScript, Perl, and PHP.
Thanks, I know `||` in general--I meant I hadn't seen the specific construction GP had used. The error handling to delete the output file in case the command failed is really elegant.