I have a pop-up window on my home computer that indicates another device on the network is using my computer's IP address. What does this mean?

I don't think it would say "accessing"? More likely it would say "using".

A computer's IP address is the number given to it by whatever is handling your network - most likely your broadband router/wireless access point. Having two or more devices using the same number can cause either one to lose access to the network - i.e.: potentially no internet, email, printing etc. You need to address this fairly quickly by determining which other device (most likely another computer or smartphone or tablet) is using the same number by simply asking everyone in your household who is on your network to access the internet etc.

If there is only you then it's possible someone is using your network without your knowledge? In which case access your router's interface and change the password for the wireless part of your network.

On a related note, if you have a lot of family devices that use your router and don't care about tracking one of them down, you can fix it easily.

1. Just click on the Apple Logo () in the top left of your screen and choose "System Preferences"

2. Click "Network" from the System Preferences window.

3. Click "Advanced..." from the bottom right.

4. Click "Renew DHCP Lease" form the "TCP/IP" pane on the window that drops down (it should already be on that pane).

5. Click "Ok" at the bottom, then "Apply" at the bottom.

That should ask the router for a new DHCP connection, which will prompt it to give you a new IP address that is not already in use.

If that fails to work for some reason, you might need some more advanced steps, or you might just track down the other device and restart it.