If using the call blocking features from My Verizon, the caller from the number you blocked will hear a short recorded message, something like the mobile subscriber has either blocked/restricted calls from this number. The call would be then automatically disconnected, not routed to voice mail. You will not receive any notification on your phone of the blocked call. Up to 5 numbers can be blocked for 90 days at a time. With a $4.99 monthly subscription to Usage Controls, 20 numbers can be blocked indefinitely.
I will add to C. Straight's reply in that Call & Message Blocking only blocks incoming calls and messages
Usage Controls blocks incoming & outgoing messages as well as calls, more like a Parental Control restricting all communication between the devices.