Introduction
Laymen explanation
Technical explanation
let's say that, device A is trying to send to device B. Instead of sending an ARP Request message, A creates an ND Neighbor Solicitation message. Now, here's where the first big change can be seen from ARP. If the underlying data link protocol supports multicasting, like Ethernet does, the Neighbor Solicitation message is not broadcast. Instead, it is sent to the solicited-node address of the device whose IPv6 address we are trying to resolve. So A won't broadcast the message, it will multicast it to device B's solicited-node multicast address.
Device B will receive the Neighbor Solicitation and respond back to device A with a Neighbor Advertisement. This is analogous to the ARP Reply and tells device A the physical address of B. Device A then adds device B's information to its neighbor cache. For efficiency, cross-resolution is supported as in IPv4 address resolution. This is done by having Device A include its own layer two address in the Neighbor Solicitation, assuming it knows it. Device B will record this along with A's IP address in B's neighbor cache.
Reference
http://www.tcpipguide.com/free/t_TCPIPAddressResolutionForIPVersion6.htm