What does this line mean in my cronjob tab?

2>&1 means "send stderr to stdout."

>>/dev/null means "append stdout to /dev/null," which is a way of hiding program output by sending it into /dev/null, whose only purpose in life is to act like a black hole for data. (Strictly speaking, for /dev/null, >>/dev/null is the same as >/dev/null.)

These rules are evaluated from right to left, so in combination they say, "hide everything output to stderr and stdout." A common mistake is to specify them in the reverse order, which will not hide the stderr output.

Also worth knowing: you can explicitly send both streams to /dev/null by saying 1>/dev/null 2>/dev/null or &>/dev/null rather than sending stderr to stdout and then sending stdout to /dev/null.

It's redirecting STDER (Standard Error) to go along with STDOUT (Standard Out). In short, both of them are redirected to /dev/null, meaning no output from the program is ever displayed.

It means redirect standard error and standard output to nothing (throw it away).