The function of DNS (Domain Name System) in internet browsing is to translate user-friendly domain names into IP addresses that computers use to identify each other on the network. When a user inputs a URL, the DNS resolves that name by querying DNS servers to find the corresponding IP address, allowing the user's device to connect to the correct server. This system simplifies the browsing experience by enabling users to remember website names rather than challenging numerical IP addresses, promoting accessibility and usability on the internet across various platforms and devices.