An IPv6 address is 128 bits. There are three types, unicast, anycast and multicast, and no broadcast. A LAN normally gets a /64 so hosts can build the 64-bit interface identifier themselves, and a site chooses DHCPv6 instead of SLAAC when it wants to control the exact address each host gets.
Types and prefixes
RFC 4291 defines unicast, anycast and multicast addresses. There are no broadcast addresses in IPv6; multicast does that job.
Prefixes to recognise: ::1/128 is loopback, ::/128 is unspecified, FE80::/10 is link-local unicast, FF00::/8 is multicast, and global unicast is everything else.
Writing addresses: "::" replaces one or more groups of 16 zero bits, and it can appear only once. 2001:DB8:0:0:8:800:200C:417A shortens to 2001:DB8::8:800:200C:417A.
Unique local addresses
RFC 4193 defines unique local addresses under FC00::/7. The L bit is set to 1 for a locally assigned prefix, so in practice these prefixes start with FD. The format is a 40-bit Global ID, a 16-bit Subnet ID and a 64-bit Interface ID.
The Global ID is generated pseudo-randomly, so each site's prefix is globally unique with high probability. A stated design goal is that sites can be combined or privately interconnected without address conflicts or renumbering. Two companies joining over a VPN, or merging, can keep their unique local prefixes. IPv4 RFC 1918 space gives no such protection, because both sides may have picked the same 10.0.0.0/8 range.
The prefix is well known so routers at site boundaries can filter it easily. RFC 4193 says these addresses are not expected to be routable on the global Internet, only within a site or between a limited set of sites.
Why a LAN gets a /64, and SLAAC versus DHCPv6
RFC 7421 explains that the addressing architecture fixes the interface identifier at 64 bits for all unicast addresses, and so for every medium that supports SLAAC. That fixes the subnet prefix at /64, whatever the site's own allocation. A company with a /48 therefore hands each office LAN a /64.
RFC 4862: the stateless approach (SLAAC) is used when a site is not particularly concerned with the exact addresses hosts use, as long as they are unique and routable. DHCPv6 is used when a site requires tighter control over exact address assignments. Both can run on the same link. Without a router, a host can only form a link-local address.
Where the exam catches people
Believing IPv6 has a broadcast address: RFC 4291 says multicast replaces broadcast.
Believing "::" can appear twice in one address: it may appear only once.
Believing SLAAC lets administrators choose each host's address: that is DHCPv6. SLAAC is for sites not concerned with exact addresses.
Believing a LAN should get a /56 or /48: those are site allocations. Each LAN gets a /64 so SLAAC works.
Believing link-local addresses suit a private network across a VPN: RFC 4291 says link-local addresses are for use on a single link. Unique local addresses are the private, routable choice.