That error means that both of your computers are using the same IP address. An IP address designates your location on the network. Since you are sharing an internet connection you are technically on a network. 2 computers cannot have the same IP address on the same network.
If you are using a DSL/Cable router it should be assigning the IP addresses to your computer when you boot it up. It may be the same address as the last time you booted or it could be different. The router is supposed to know which IP addresses are in use so it doesn't duplicate them and give the same one to another computer. In your case either your router is having a problem or one of your computers has a static IP address and the router is trying to give that same address to your other computer. A static is an IP address that is manually assigned to the computer and never changes unless you change it manually.
On both computers make sure you don't have static IP addresses. Go to Control Panel and then Network and Sharing Center. Then click on Change adapter settings and right click your Ethernet or wireless connection and choose Properties. Double click Internet Protocol Version 4 (TCP/IP) and make sure Obtain an IP address automatically and Obtain DNS server address automatically are checked. If they are checked already then its most likely your router is having problems with its DHCP which is the service that assigns IP addresses to your computers.