$1 is a placeholder for the caller's number. This is used for Auto Attendant Callback. If the caller hangs up before the auto attendant answers, then the auto attendant will call the caller's number and offer the usual options.
In this configuration:
{(1555333222x):aa($1)}
If the caller is 15553332221, then the aa will call back to 15553332221 using the Auto Attendant Primary Line.