DNS records are the records on your name server that tells requests made to your domain name the address it should request the resources.
How DNS Records Work
Every registered domain declares a name server. The name server provides DNS records that list where resources are located.
Here's an example
Let's say you have a domain name. Someone wants to visit your website so they type your domain name into their browser. The browser needs to know the address of the computer where the files for your website are stored. To find that out, the browser looks up the name server for your domain, requests the A record on it and makes a request to the IP address in your a record for your website file and returns it to the viewer.
What else do DNS Records Do
There are a lot of different types of records and purposes for them. A very common record type is an MX record, or "Mail Exchange" record. This identifies the email servers that handle email for a domain.