DNS stand for Domain Name Service (or Server or System) and works like a phone book for the Internet. It translates names such as "www.youtube.com" into an IP address so your request can be routed to the appropriate destination.
Normally, DNS is provided by your ISP. But the use of a third-party DNS (e.g., Google) is also popular. Most often, the DHCP response from your home router will specify the DNS servers it learned from your ISP. Or, it may specify its own address for DNS so it can "proxy" the requests to the actual servers.