Ordinary DNS goes from name to address. Reverse DNS does the opposite: given an address, which name belongs to it? That answer lives in a PTR record, published by whoever operates the IP range.
The arpa notation
Reverse DNS uses a namespace of its own. The address 8.8.8.8 is looked up as 8.8.8.8.in-addr.arpa — the octets reversed. IPv6 does the same per hexadecimal character, under ip6.arpa, which produces long names.
Why mail servers care
A receiving mail server often checks whether the address has a PTR record, and whether the name in that record resolves back to the same address. That is forward-confirmed reverse DNS. When it does not match, it is one of the signals that gets mail marked as spam.
No PTR is not an error
Reverse DNS is nowhere mandatory. Consumer connections often have a generic PTR record from the provider, or none at all. Only someone sending mail from an address has real reason to set one up — and can ask the operator of the range to do it.