A floating IP is a special type of Virtual IP that enables failover to provide High availability in a cluster. In a floating IP configuration, only one of the nodes in the cluster “owns” and advertises the IP address at a time. When the node that owns the IP fails, the IP can then be advertised by another node in the cluster, thus moving (or floating) the IP to the new node.
A floating IP by itself is just a concept. The implementation of this setup depends on tools that implement the VRRP protocol to do healthchecks on the cluster nodes and move the IP in case of node failures. Keepalived and HAProxy both implement the VRRP protocol and can be used to manage a VIP to provide a floating IP behavior.
The software that manages the VIP uses ARP broadcasts (or announcements) to inform the switches and other hosts on the network that the MAC address associated with the VIP resides on a particular node. When the host that currently holds the VIP (aka the master) fails, the next highest priority node is assigned as the new master and issues an ARP broadcast to advertise that now it holds the VIP.
References
What is a Virtual IP Address? How does it help with High-Availability