What must computers share in order to communicate with each other?

Internet is needed for computers to communicate with each other.

INTERNET - Is an electronic communications network that connects computers network worldwide.

- the most popular modern communication tool.

- is a giant network.

Another Answer

All that's needed for computers to communicate is a pair of wire connected to a communication port and software to drive some protocol. There are many ways for computers to communicate with each other. The internet is "the most popular modern communication tool", but it is not the only way to transfer data.