What is the full-form of ATA?
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 While the ATA 100 numbering system has been superseded, it continued to be widely used until it went out of date back in 2015, especially in documentation for general aviation aircraft, on aircraft Fault Messages (for Post Flight Troubleshooting and Repair) and the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.