Internet Protocol Address. Every computer connected to the internet has an IP address. Some websites and servers have unique IP addresses, but most web hosts host multiple websites on a single host.
Many SEOs refer to unique C class IP addresses. Every site is hosted on a numerical address like aa.bb.cc.dd. In some cases many sites are hosted on the same IP address. It is believed by many SEOs that if links come from different IP ranges with a different number somewhere in the aa.bb.cc part then the link may count more than links from the same local range and host.