What is an IP address?IP addresses are four sets of numbers separated by periods that allow computers to identify each other on a network - for example 192.168.0.10. Every computer has at least one ip address, and two computers should never have the same ip address. If they do, neither of them will be able to connect to the internet/network.
If you have a wireless / wired router it will have an IP address (usually 192.168.0.1) and it will issue the next number to each pc that connect so: 192.168.0.2 then 192.168.0.3 etc.. so if you are setting static IP addresses for any reason jump ahead to something like 192.168.0.100 then you should never have any conflicts.
Dynamic vs Static IPsMost routers assign dynamic IP addresses by default. They do this because dynamic ip address networks require no configuration. The end user can simply plug their computer in, and their network will work. When ip addresses are assigned dynamically, the router is the one that assigns them. Every time a computer reboots it asks the router for an ip address. The router then hands it an ip address that has not already been handed out to another computer. This is important to note. When you set your computer to a static ip address, the router does not know that a computer is using that ip address. So the very same ip address may be handed to another computer later, and that will prevent both computers from connecting to the internet. So when you asign a static IP addresses, it's important to assign an IP address that will not be handed out to other computers by the dynamic IP address server. The dynamic IP address server is generally refered to as the dhcp server.
You can read alot more about IP addresses here: http://en.wikipedia.org/wiki/Ip_address
You may want to set static IP addresses for each of your pcs if you have other items connecting to your network like NAS drives or Media Players as these can often use a static address that may clash with a pc that is already connected (for example). A static IP address is also required if you are using a Torrent server and have to set up port forwarding to download.