"Internet" is a proper noun.

It refers to a specific thing.

This means that it is capitalized (spelled with an upper-case 'I').

The lower-case variant, "internet," is only acceptable in rare situations where one is referring to a computer network that uses "internetworking" technologies such as Internet Protocol (IP), but which is not connected to the Internet. It could also be used to discuss generic or conceptual internetworks, such as "TCP/IP can be used on internets to transmit data."