Reverse DNS is what maps an IP address to a host name. A PTR-record type is used to store reverse DNS entries. The name of the PTR-record is the IP address with the segments in reverse order followed by ".in-addr.arpa".
For example the reverse DNS entry for IP 2.3.4.5 would be stored as a PTR-record for "5.4.3.2.in-addr.arpa". That then points to "somehost.yourdomain.tld".
It's important for things like email, where the receiver can do a reverse DNS lookup to make sure your host is supposed to be sending email from "example.domain". Lacking proper reverse DNS, your outgoing email could be marked as spam. Or rejected outright for one not existing. It's also used for some forms of SPF entries (though that's discouraged).
Last, it's somewhat useful for logs if you have hosts in your domain that connect to each other. Though, usually, you're encouraged NOT to configure apache, syslogd, etc, to do reverse DNS lookups...for performance reasons.
