These addresses are globally unique. The format is shown below.
Prefix Subnet ID Interface ID
48 Bits 16 Bits 64 Bits
The 16 bits in the subnet field allows you to create 65,536 subnets. You can have 4 times as many host address (the interface ID part of the address) per subnet. Although its crazy to have such large subnets, its now very clear that the first 48 bits are the prefix, the next 16 bits are the subnet, and the last 64 bits are the hosts. It helps chop out the confusion of VLSM for many new network engineers, because there is now a clear delineation between what is the network address, what is the subnet, and what is the host part of the address.
We can quickly identify a global IPv6 address, by looking whether the address starts with a 2 or 3. If it does, its a global address. If not, it aint.
The techy way of working this out is by breaking down the first 16 bits of a global IPv6 address, for example 2001::1/64, it would be 2001. If we convert this from hex to binary we get 0010 0000 0000 0001. The first 3 bits of any global IPv6 address always start with 001. So you can see, that a global address is always going to start either a 2 (0010) or a 3 (0011).