SLAAC makes it much easier to get hosts up and running, since they don't need DHCPv6, and assign all of their addresses themselves. You can still rely on DHCPv6 to manage your static addresses.

Subnetting is way easier, because you're never dealing with anything smaller than a /64, and all subnets are done on hex boundaries.

It no longer has broadcasts, and has a more efficient header.

There is no more fragmentation done through routers, which gives some security benefits (can't rely on it as a way to bypass firewalls that cannot automatically reassemble packets before passing them) and provides better performance. End-to-end Path MTU is determined through ICMPv6 messages (so make sure you allow those on your ACLs!)

Ping sweeps become harder, since your typical IPv6 subnet is bigger than the entire current IPv4 addressing space. (2⁶⁴ vs 2^32). Well spaced address blocks for your statically assigned addresses can make a ping sweep an almost futile effort, and for self-assigned addresses, the address is entirely dependent upon the host's MAC address.

Multicasting is a much bigger deal in IPv6, since broadcasting doesn't exist.

ICMPv6 also plays a much bigger role, since the v6 ARP/RARP equivalent, the aforementioned Path MTU, and a host of other important things are all rolled into it.

A interface/device can now not only have more than one address assigned to it, but is guaranteed to have at least three minimum; usually there quite a few more, but it depends on the device (see scopes below).

There are now three primary address scopes:

Global Unicast addresses are pretty self-descriptive; the current allocated space for them is 2000::/3. It's the equivalent of any public IPv4 address

A subset of these are Anycast addresses, which are one-to-closest addresses which can be assigned to many devices, all of which can process a request directed to them. Think of how root DNS servers work now, and you've got a good idea of these. These addresses cannot be distinguished from other global unicast addresses

Multicast addresses are also pretty self-explanatory. They fall under the range FF00::/12, and have their own individual set of scopes (not going into details here, look it up if you want more)

Link-Local Unicast addresses are bit trickier to grasp initially; falling under the range FE80::/7, they are addresses whose scope is limited to the local subnet only. They're used for a number of things, like during address initialization, routing protocol updates, neighbor and router discovery (the former being the v6 ARP equivalent), and many other things. Again, won't go into a ton of detail, you can look it up on your own.

Each device, assuming it connects to the internet in some way, will have at least one address from each of these scopes, although as I said, they can have many many more.

People also like to say IPv6 is more "secure" since all devices that run IPv6 must also support IPSec, but that doesn't really amount to much.

Those are the biggest highlights I can think of off the top of my head, but there are plenty more I've missed. Think that gives you some stuff to read up on anyway :)