"Padding" is EDNS(0) Option code 12, and is used to pad DNS messages (queries as well as responses) to a desired size.
Padding is used in situations where the DNS traffic is encrypted, but size based correlation of encrypted DNS messages could still be used to reconstruct the original query and response information. Padding DNS messages makes it harder to apply size based correlation with known unencrypted messages
The EDNS(0) "Padding" Option was specified by the IETF "dprive" working group, and published in RFC 7830. Subsequently, Padding Policies were described in RFC 8467
2018-01-17: A new revision of the EDNS(0) Padding Policy draft was submitted to the IETF DPRIVE working group. The document subsequently went to "Working Group Last Call", and will hopefully become an RFC over the next few months.
2017-09-13: BIND 9.12.0 will support EDNS0 padding - see the release notes
2017-01-25: Knot Resolver (v1.2.0) now supports EDNS Padding out of the box - see the release notes
2016-12-05: First working group revision of Padding Policy for EDNS(0) is published. This is essentially a 1:1 copy of the previous individual draft (under a new name).