IP address
An IP address serves two principal functions. It identifies the host, or more specifically its network interface, and it provides the location of the host in the network, and thus the capability of establishing a path to that host. Its role has been characterized as follows: "A name indicates what we seek. An address indicates where it is. A route indicates how to get there."
The header of each IP packet contains the IP address of the sending host, and that of the destination host.
Anonymity
However, the Internet was not designed for anonymity: IP addresses serve as virtual mailing addresses, which means that any time any resource on the Internet is accessed, it is accessed from a particular IP address, and the data traffic patterns to and from IP addresses can be intercepted, monitored, and analysed, even if the content of that traffic is encrypted. This address can be mapped to a particular Internet Service Provider (ISP), and this ISP can then provide information about what customer that IP address was leased to. This does not necessarily implicate a specific individual (because other people could be using that customer's connection, especially if the customer is a public resource, such as a library), but it provides regional information and serves as powerful circumstantial evidence.