IP address conflict on home network with two laptops?

We have just added a second laptop to our home network. A network error come up on the new laptop when closing down internet explorer saying 'IP address conflict. Another computer on this network is using the same IP address' or something like that.
But both of the laptops are able to connect to the internet and at the same time too.
I heard that two computers should never have the same IP address as results can be unpredictable. What does that mean?
Do I need to fix this? And if so how?

This occurs when two or more computers on the same LAN network end up with the same IP address. Usually,when this occurs, both computers end up not being able to connect to network.This may be the only problem and no other issues apart from this.If you are able to connect to internet then no problem...but if it is interrupted...There are a few ways in which this problem can be fixed.If it is Static IP request your ISP for a change of IP.If it is a Dynamic IP you can try resetting your modem by switching ON and OFF the modem or open the command prompt and type "ipconfig /release," which dumps the automatic address it had, and then "ipconfig /renew," which gets a new address.To check for the change in IP you can visit Ip-details.com which gives your public Ip when you visit the site.