Does gratuitous ARP work like a normal ARP request?
Why is gratuitous ARP used for HSRP?
Gratuitous ARP is a sort of "advance notification", it updates the ARP cache of other systems before they ask for it (no ARP request) or to update outdated information.
When talking about gratuitous ARP, the packets are actually special ARP request packets, not ARP reply packets as one would perhaps expect. Some reasons for this are explained in RFC 5227.
The gratuitous ARP packet has the following characteristics:
Gratuitous ARP is used for some reasons:
As for the second part of your question, HSRP, VRRP etc. use gratuitous ARP to update the MAC address tables on L2 devices (switches). Also there is the option to use the burned-in MAC address for HSRP instead of the "virtual"one. In that case the gratuitous ARP would also update the ARP tables on L3 devices/hosts.
If you want some video there is a Great explanation here.