Q:

What is a TAI64 time format?

While going through the Logstash date plugin documentation at
https://www.elastic.co/guide/en/logstash/current/plugins-filters-date.html#plugins-filters-date-match
I came across TAI64N date format. 
Can someone please explain about this time format?

A:

TAI stands for Temps Atomique International, the current international real-time standard. One TAI second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium atom. TAI also specifies a frame of reference. 
From Toward a Unified Timestamp with explicit precision
TAI64 defines a 64-bit integer format where each value identifies a particular SI second. The duration of SI seconds is defined through a known, precise count of state transitions of a cesium atom. Time is structured as a sequence of seconds starting January 1, 1970 in the Gregorian calendar, when atomic time (TAI) became the international standard for real time. The standard defines 262 seconds before the year 1970, and another 262 from this epoch onward, thus covering a span of roughly 300 billion years, enough for most applications.
The extensions TAI64N and TAI64NA allow for finer time resolutions by
referring to particular nanoseconds and attoseconds (10-18s), respectively, within a particular second.
While TAI64 is compellingly simple and consistent, it has to be extended not only
with regard to fine resolutions, but in other ways as well. 

It is only concerned with time-points, but a complete model of time needs to address the interrelation of time-points and intervals as well. Most models conceive intervals as sets of consecutive timepoints. This creates the obvious transformation problem - assuming a dense time domain - that no amount of time-points with a postulated duration of 0 can yield an interval with a duration larger than 0, and that even the shortest interval is a set of an infinite number of time-points.
TAI64 does not address uncertainty with respect to time. 
It emphasizes monotonically-increasing continuity of time measurement. Human perception of time, however, is shaped by less regular astronomical phenomena.

Precisely, TAI64 format is better for various reasons such as,

International Atomic Time
Strictly monotonic (no leap seconds)
64-bit uint #seconds from epoch
32-bit uint #nano-seconds (TAI64N)
32-bit uint #atto-seconds (TAI64NA)

You can read further on, Bernstein D.J. 2002. "TAI64, TAI64N, and TAI64NA,

TAI64, TAI64N, and TAI64NA
TAI and real time
TAI64 labels and external TAI64 format. A TAI64 label is an integer
  between 0 and 2^64 referring to a particular second of real time.
  Integer s refers to the TAI second beginning exactly 2^62 - s seconds
  before the beginning of 1970 TAI, if s is between 0 inclusive and 2^62
  exclusive; or the TAI second beginning exactly s - 2^62 seconds after
  the beginning of 1970 TAI, if s is between 2^62 inclusive and 2^63
  exclusive. Integers 2^63 and larger are reserved for future
  extensions. Under many cosmological theories, the integers under 2^63
  are adequate to cover the entire expected lifetime of the universe; in
  this case no extensions will be necessary. A TAI64 label is normally
  stored or communicated in external TAI64 format, consisting of eight
  8-bit bytes in big-endian format. This means that bytes b0 b1 b2 b3 b4
  b5 b6 b7 represent the label b0 * 2^56 + b1 * 2^48 + b2 * 2^40 + b3 *
  2^32 + b4 * 2^24 + b5 * 2^16 + b6 * 2^8 + b7.
For example, bytes 3f ff ff ff ff ff ff ff hexadecimal represent the
  second that ended 1969 TAI; bytes 40 00 00 00 00 00 00 00 hexadecimal
  represent the second that began 1970 TAI; bytes 40 00 00 00 00 00 00
  01 hexadecimal represent the following second. Bytes 40 00 00 00 2a 2b
  2c 2d hexadecimal represent 1992-06-02 08:07:09 TAI, also known as
  1992-06-02 08:06:43 UTC.

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