As Konrad Rudolph points out, there is no such thing as a trailing backslash. (With the usual category codes,) A backslash is an escape character, and must be escaping something. In this case, it's escaping the following line break, which, if I remember correctly, is usually interpreted to mean the same as an escaped space, which, again if I remember correctly, is used to tell TeX that you want exactly one space where it might otherwise put 0 or more than 1:
$bad\ way\ to\ put\ text\ in\ math\ mode$
(UPDATE: Probably a better example is the traditional use to prevent space-swallowing after a macro, as in
\TeX\ is fascinating.) As Ulrike points out above, your original document attempts to pass the macro
\maketitle as the second argument to \author, which breaks somewhere down the line (presumably when
\@@AbstractAuthor is used); whereas the fixed document instead passes the macro
\<par> as the second argument, which'll probably compile, but will put a space everywhere the abstract-author's name might be expected.