An A Record, which stands for Address Record, is a type of DNS record that maps a domain name to an IP address (IPV4). An example would be when you type in 1903Studios.com you are actually being sent to 126.96.36.199. The A Record is what allows you to remember names instead of numbers for websites on the internet. When people think of DNS, this is typically what they think of first.
There are several types of sub A Records that deal with IPV6 and connecting IPV4 to IPV6, but these are typically taken care under the hood.