Terms
Domain Name System
The directory that turns a domain name into the address of an actual server.
Computers find each other using IP addresses, which are numbers. People use names. DNS is the system that translates between the two.
When someone types your domain, their computer asks DNS where that name points, gets back an address, and connects there.
Where you meet it
DNS records are what you edit when you point a domain at a new host, or set up email. The common ones are A (points at a server), CNAME (points at another name), and MX (where email goes).
Changes take time to spread, from minutes to a day. That delay is called propagation, and it is the reason a site move is not instant for everyone.
External resources