Silent Post is another approach Hosted Checkout offers to handle transaction results - the other two being Receipt Link and Relay Response.
If you know about Receipt Link (just display the standard E-xact receipt) and Relay Response (receive results from E-xact then send response to E-xact to display to the customer) then it's easier to think of Silent Post as kind of a hybrid between those methods.
With Silent Post E-xact will relay the transaction results back to the merchant's server but unlike Relay Response, we are not expecting an answer back. Similar to Receipt Link, the customer will instead be shown the standard E-xact receipt (whether the transaction is approved or declined).
Note that Silent Post is very similar to the Receipt Link POST method except that Receipt Link requires the user to click a link to invoke the method.