Accreditation points are your way of knowing that the stats you're looking at are legitimate. Here is how the program works...
You receive accreditation points from other geocachers. You in turn should do the same. After some time each user should have some points on their account. These points form a circle of trust so that you can say that this geocacher is honest about their stats. This doesn't mean that users with no accreditation points are dishonest. What it means is that if you have a large number of geocaches listed in your stats, you have people that can vouch for the validity of them. It's not a perfect system but it reduces the probability of fraud, here is why.
Let's say someone creates an account with 2000 geocaches. They have no accreditation points. After a few months they still don't have any. The state moderator cant contact them or verify the numbers on any geocache site. The moderator may remove those stats because they really cant be substantiated. It's unlikely that such a user (who created the fraudulent stats) would go and create 10-20 accounts to create a circle of trust. Additionally, if they did, it makes it easier for the moderator to go and delete all associated stats as well.
What do the colors mean in the stars? Here is a breakdown
Less than 5 accreditation points
5 - 9 accreditation points
10 - 49 accreditation points
50-99 accreditation points
100+ accreditation points
Right now these acrediation points can be seen at the bottom of any users stat page. Simply click on the link for any users name and it will show their stats along with their accredation points at the bottom of the page. For example you'll see
This member has 0 accreditation points
At the top of each user page you can see where you can acredit the user yourself. You'll need to be logged in to use this feature. Simply click the "Accredit User" link next to the users name. For Example you'll see
Geocacher Details for Ventura_Kid (Ventura Kid) [ Accredit User ]
Once you click that link you'll be taken to the page to accredit that user.