What's Linux test -a command test for?

I am not sure why the info page doesn't have it, but running help test in bash gives the answer:

...
    File operators:

  -a FILE        True if file exists.
...

So it is simply an "existence" test, no other permissions/attributes checked.

If you're running test or [ in bash, it's actually probably the built-in version, and not the coreutils version in /usr/bin:

$ type test
test is a shell builtin
$ type [
[ is a shell builtin

That said, it does appear that the coreutils version implements both -a and -e, with exactly the same behavior. Maybe -a is not reflected in the manpage because it's not standard, so maybe it was added later and that person neglected to update the manpage accordingly. But I can't say I know the history behind why it was added (or even what the a is supposed to be short for).