Some cable modems cause this when they temporarily lose link to the ISP.
Your cable modem probably temporarily lost its DOCSIS WAN link to your cable ISP, so it went into a kind of backup mode of acting as a local DHCP server, serving out private IP addresses, so that if you didn't have a router behind it, your home network could still continue to function, since those DHCP clients would still be getting addresses, albeit local/private ones.
After the DOCSIS link to the ISP comes back up, the cable modem should stop serving out private IP addresses, so your base station should be able to get a public IP address and be back to normal. However, it's possible that the Double NAT warning didn't get automatically cleared, even though the underlying condition already got cleared up.
Reboot your AirPort base station and then use the AirPort Utility to see what WAN IP address your base station has. If it's a public IP address, then everything is good again. If it's a private IP address, then yes, you somehow have an upstream box doing NAT, and you should probably figure out your double NAT situation.
Private IP addresses come from the following ranges:
10.0.0.0 through 10.255.255.255
172.16.0.0 through 172.31.255.255
192.168.0.0 through 192.168.255.255
Your AirPort base station has very good NAT code compared to your average home networking device, so if you have to run NAT somewhere, it's generally best to make your AirPort base station your single NAT device. So you definitely ought to figure out what's going on, and make sure your ISP or your cable modem aren't doing NAT.