The technology that allows for asynchronous communication over the internet is called WebSockets. WebSockets enable a persistent, full-duplex connection between a client and a server, facilitating real-time data exchange without the need for constant HTTP requests. This technology is particularly beneficial for applications requiring instant updates, such as chat services, online gaming, and live notifications. By allowing both parties to send and receive messages independently, WebSockets enhance user experience by providing smoother interactions and reduced latency in communication over the web.