The more I look at this PDF (Application Binary Interface for the ARM Architecture: The Base Standard) the less I understand what it means. Also I'd like some comments on Procedure Call Standard for the ARM Architecture and ELF for the ARM Architecture.
An ABI (Application Binary Interface) is a standard that defines a mapping between low-level concepts in high-level languages and the abilities of a specific hardware/OS platform's machine code. That includes things like:
The answers to these are:
Without some kind of this standardization, (machine) code created by different compilers couldn't use the same kind of libraries (how would you know in which way the library code expects function arguments or data structures to be passed ?).
Every platform (a combination of specific hardware, operating system software and code written in specific programming languages / compiled with specific compilers) defines a whole set of ABIs to make things interoperable. The terminology in this area isn't clear, sometimes people just talk about "the ABI", other times it's called the "platform supplement", or one mentions the programming language and says e.g. "the C++ ABI". Keep in mind, there is not one such thing.
The documents that you linked to in your question are all specific examples of this (language- / operating-system / hardware-specific ABIs).
Even on a specific platform, there's no necessity to have one and only one ABI (set) because different such conventions might have different advantages (and therefore provide better performance / smaller code / better memory usage / ... - depending on the program) and system designers usually try to be flexible / permissible.
On 32bit Microsoft Windows, for example, there's a multitude of ABIs (fastcall, stdcall, pascal, ...) for the function calling convention parts.
Anyway, a generic stackoverflow search for "ABI" (included the links under the "Related" sidebar) gives so many leads to researching this question that I close my answer at this point.