De acordo com man bash
:
Words of the form $'string' are treated specially. The word expands to string, with backslash-escaped characters replaced as specified by the ANSI C standard. Backslash escape sequences, if present, are decoded as follows: \a alert (bell) \b backspace \e \E an escape character \f form feed \n new line \r carriage return \t horizontal tab \v vertical tab \ backslash \' single quote \" double quote \? question mark \nnn the eight-bit character whose value is the octal value nnn (one to three digits) \xHH the eight-bit character whose value is the hexadecimal value HH (one or two hex digits) \uHHHH the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHH (one to four hex digits) \UHHHHHHHH the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHHHHHH (one to eight hex digits) \cx a control-x character The expanded result is single-quoted, as if the dollar sign had not been present.
Consequentemente, $'s/\r$//'
exclui um ASCII CR
no final da linha. É uma maneira grosseira de converter as terminações de linha do Windows em finais de linha do UNIX.