I live in a shared house. And my ZoneAlarm firewall keeps giving me an alert message. What does it mean?

It sounds like another PC in your house is trying to connect to your one. Find out which PC it is from the IP address (you can go to a command prompt and type ipconfig to find this) and see if there's any software on there that is poking around on the network. Alternatively, it could be that user trying to do something to the other PCs or possibly a virus trying to infect other machines on the network, so some checking may need to be done. Or it could just be windows trying to establish some network connectivity with any other machines it can see on the network.