All the computers connected to the internet are identified by a unique series of numbers called IP addresses (eg. 184.108.40.206). IP stands for Internet Protocol and these numbers are not easy to remember. Domains were invented because we find it easier to deal with the names, than numbers.
To make it easier to connect specific computers and content, the Domain Name System (DNS) was invented. This is basically an address book which is used to map an easy to remember domain name to an IP address. This then allows any responses sent to the domain name to communicate with the computer that the IP address relates to.
Using DNS is similar to making a phone call with your mobile phone. Your phone dials the number for you and the telephone network uses that number to connect you.