It means that every LAN should get an IPv6 /64. Deviating from that will cause auto-configuration to break, and is therefore strongly discouraged.
IPv6 allocations (and assignments) should be done in much larger blocks. In "Internet Registry Speak" an allocation is usually done to an ISP while an assignment is usually done to an end-user. Therefore usually allocations are much larger than assignments, because an ISP needs a big block to make assignments from to its customers.
- A common minimum allocation size is a /32, meaning that an ISP can get more like a /29 or even bigger if they need it.
- A common assignment size is a /48 per end-user site.
- And as you said the standard subnet/LAN size is /64
Based on these sizes, an ISP can assign 65536 /48s amongst its customer's sites. Each of those sites can then configure up to 65536 LANs with a /64 from that /48. These might sound extremely large, but IPv6 is designed to prevent people from even getting a block that is too small for them. Plenty addresses always have to be available, on each level.
Now, for a home user, 65536 LANs might be a little more than they need. Some ISPs have therefore decided to give them only a /56. That allows for 256 LANs per customer site (a home in this case). This is considered acceptable as well, but only for home (residential) customers.