IPv6 has moved away from LAN-layer broadcast, instead providing a wide range of LAN-layer multicast groups. (Note that LAN-layer multicast is often straightforward; it is general IP-layer multicast (20.5 Global IP Multicast) that is problematic. See 2.1.2 Ethernet Multicast for the Ethernet implementation.) This switch to multicast is intended to limit broadcast traffic in general, though many switches still propagate LAN multicast traffic everywhere, like broadcast.
An IPv6 multicast address is one beginning with the eight bits 1111 1111 (ff00::/8); numerous specific such addresses, and even classes of addresses, have been defined. For actual delivery, IPv6 multicast addresses correspond to LAN-layer (eg Ethernet) multicast addresses through a well-defined static correspondence; specifically, if x, y, z and w are the last four bytes of the IPv6 multicast address, in hex, then the corresponding Ethernet multicast address is 33:33:x:y:z:w (RFC 2464). A typical IPv6 host will need to join (that is, subscribe to) several Ethernet multicast groups.
The IPv6 multicast address with the broadest scope is all-nodes, with address ff02::1; the corresponding Ethernet multicast address is 33:33:00:00:00:01. This essentially corresponds to IPv4’s LAN broadcast, though the use of LAN multicast here means that non-IPv6 hosts should not see packets sent to this address. Another important IPv6 multicast address is ff02::2, the all-routers address. This is meant to be used to reach all routers, and routers only; ordinary hosts do not subscribe.
Generally speaking, IPv6 nodes on Ethernets send LAN-layer Multicast Listener Discovery (MLD) messages to multicast groups they wish to start using; these messages allow multicast-aware Ethernet switches to optimize forwarding so that only those hosts that have subscribed to the multicast group in question will receive the messages. Otherwise switches are supposed to treat multicast like broadcast; worse, some switches may simply fail to forward multicast packets to destinations that have not explicitly opted to join the group.