I was going through FCOM of A320 and came to know that FCOM chapters are called as ATAs. So first of all what is its full- form and secondly why do we call the chapters ATAs ?
ATA stands for Air Transport Association (today called Airlines for America). The numbering standard is called ATA 100 and was widely used for various types of aviation documents and manuals from 1956 until 2015 according to Wikipedia:
ATA 100 contains the reference to the ATA numbering system which is a common referencing standard for commercial aircraft documentation. This commonality permits greater ease of learning and understanding for pilots, aircraft maintenance technicians, and engineers alike. The standard numbering system was published by the Air Transport Association on June 1, 1956. While the ATA 100 numbering system has been superseded, it continued to be widely used until it went out of date back in 2015, especially in documentation for general aviation aircraft, on aircraft Fault Messages (for Post Flight Troubleshooting and Repair) and the electronic and printed manuals.
The basic function of ATA 100 was a system to categorize systems, subsystems and sub-subsystems etc, to a universal standard. This allows the same numbering convention to be applied across documentation where they follow the ATA 100 standard. This can extend down to an OEM's engineering drawing system, as well as internal and external documentation.
So for Flight Controls, with the assigned ATA100 number of Chapter 27, you know that Maintenance Manual sections, Parts Manual section, FCOM sections, Service Bulletins, OEM internal work documentation, pretty much anything connected to flight control systems, can be found the indexing system at Chapter 27, or some number prefixed with 27.
I worked at an OEM that didn't use ATA100 for its engineering drawing system, so it's drawings were categorized under some other convention. If you wanted to search for a Flight Controls drawing, you had to look up an index to find where to look because the numbering was something someone made up. It was quite a pain until you memorized that particular drawing system.
For an ATA100 compliant drawing system, if you were already familiar with ATA 100, you knew that flight controls drawings would all start with 27 as the first 2 digits of the drawing number, and subsequent numbers would also follow the ATA100 sub-system convention. It makes things much easier to find and you knew where to look in any manual or document of any OEM that follows the standard.