An A Record — more accurately, a 'DNS A Record' — links a domain to an IP address.
Your A Record — the 'A' is short for 'address' — links your chosen domain to the IP address of the system that hosts that domain.
For example, if your domain and subdomain is marketing.example.com, and your dedicated IP address is 101.10.10.101, then any attempt to access marketing.example.com — from a web browser, say, or by using curl at the command line — will be transparently routed to 101.10.10.101. The browser will send a query to a DNS server, which uses the A Record to determine the target IP address. The DNS server returns this address to the browser, which uses it to request the web page.
The A Record is a file. It contains the domain, the target IP address, the record type, a TTL (Time to Live) value which indicates how long changes made to the record can be expected to take effect, and a subdomain value. This can be an actual subdomain — marketing in the example above — or a symbol: * to indicate all possible subdomains, or @ to specify the root domain.
A Records only hold IPv4 addresses. If your website has an IPv6 address, it will instead use a AAAA Record.