Yes I can.
IPv4, due to the size of the address pool, has long had a technique called Network Address Translation. In a simplistic view, let's assume you are allocated the (invalid) IP address for your router 256.10.20.30
(I use invalid addresses so people don't go around pinging them etc). Locally, your router is 192.168.0.1
and your host is 192.168.0.2
like this:
/----------\ /-------------------------------\ /----------------\
| Internet |-------| Your router |-------| A computer |
\----------/ | Internet sees as 256.10.20.30 | | has only: |
| You see as 192.168.0.1 | | 192.168.0.2 |
\-------------------------------/ \----------------/
As such, your router appears to the internet as a public facing IP-address; however, unless you deliberately route connections on ports from the router to a computer on the private IP address range, the computers on the private LAN side are not directly addressable from the internet. The route is performing two functions - both NAT and routing.
In IPv6 there are a lot of addresses. The idea fundamentally is that there are no private IP address ranges (which isn't exactly true; an RFC for that does exist) and as such the IPv6 situation looks like this:
/----------\ /-------------------------------\ /----------------\
| Internet |-------| Your router |-------| A computer |
\----------/ | Internet sees as 2000::... | | has: |
| You see as 2000::... | | 2001::... |
\-------------------------------/ \----------------/
There isn't really enough space in these boxes to write out the full addresses, but in the IPv6 model, the router performs its routing function (it gets packets to the computers on the LAN) but crucially here it routes both from and to the internet, rather than routing / NATing outwards.
The effect of this is that the default case for IPv4, namely that home computers aren't directly accessible by nature of the fact they have no IP address unless the router knows about the connection goes away. The computer becomes addressable from the internet, much like a server.
Clearly, such connections can still be firewalled, with firewalls denying all incoming (non-client-initiated) connections, however, you've lost needing to explicitly configure your router to route internet packets to you. If the firewall doesn't filter the incoming packet, the client better be able to cope with it. There is, therefore, a slightly increased security risk to home users using IPv6.
I expect (hope?) most home routers will come configured with this firewall setting. As such, while the risk is slightly increased, it is still probably dwarfed by the threat from browser-based exploits (the "outbound stuff").