>> /dev/null redirects standard output ( stdout ) to /dev/null , which discards it.
(The >> seems sort of superfluous, since >> means append while > means truncate and write, and either appending to or writing to /dev/null has the same net effect. I usually just use > for that reason.)
2>&1 redirects standard error ( 2 ) to standard output ( 1 ), which then discards it as well since standard output has already been redirected.
This way you can suppress all messages that might be issued by the executed command. In cron this is often done to avoid being spammed by lots of irrelevant messages from service scripts. Nevertheless be careful with this as some messages might be important.