Acronym: Internet Protocol
Internet Protocol version 4 addresses are 32-bit numbers often expressed as 4 octets in "dotted decimal" notation (eg, 192.168.45.230). The organisation currently responsible for administering IP addresses is ICANN. An upcoming challenge is that some name spaces are reaching capacity limits with IPv4. This is one of the reasons why IPv6 was invented, which also solves some security problems related to IPv4.
Note that an IP address is freely published across the net. There are legal and freely available systems in place to link an IP to one's real-world information. One is not anonymous simply because one's name and mailing address aren't sent alongside it.
IPv6 is 128-bit.