Static IP address is an IP address you set manually and it will stay like that.
Pros: Known permanant address (good for services, not so much an issue for clients)
Cons: Extra work
Getting an address assigned automatically will give you an IP address which will change dynamically, but you don't have to set it.
Set DHCP on in where you have network settings and if your router is set to assign addresses (it is a DHCP server)...then your xbox, pc and ps2 will get an address automatically from it.
All programs with network settings always have these two options for IP addressing.