A DNS (Domain Name Server) is like a telephone directory, but for computers.
For example, you can dial someone’s telephone number to speak to them, but it’s not very practical to remember a random sequence of numbers and it’s much easier to just look up the name of the person you want to talk to in the phone book.
Now imagine that everyone in the world could have only one unique name, and that this name would be assigned a unique telephone number. So instead of remembering the number, all you have to do is know the name and you can look up the number – this is what a DNS does for a domain name and it’s IP address.
When you type “google.com” in your internet navigator (Internet explorer/Firefox/Chrome, etc.), your computer will ask your DNS what the IP address of “google.com” is and your DNS will reply with “188.8.131.52”. Your internet navigator will then connect to google.com using the IP 184.108.40.206.
This all happens in the background; all the user is aware of is typing ‘google.com’ into the address bar and then seeing the Google homepage.
However, if you know the IP address and not the domain name, then you could go directly to Google by typing in http://220.127.116.11 if you wanted.
When you connect to the internet at home, your modem will use the DHCP server to provide with your IP address, and also a list of DNS servers for looking up domain names.