The function of a DNS server in internet browsing is to translate friendly domain names into IP addresses, which devices require to communicate over the internet. When a user types a URL into a browser, the DNS server resolves the domain name, directing the browser to the correct IP address of the desired website. This process is essential for seamless internet navigation, enabling users to access content without needing to remember complex numerical addresses. DNS servers play a crucial role in maintaining the overall functionality of the internet.