Once upon a time, people had terminals like typewriters (with only upper-case letters, but that's another story). Search for 'Teletype', and how do you think tty got used for 'terminal device'?
Those devices had two separate motions. The carriage return moved the print head back to the start of the line without scrolling the paper; the line feed character moved the paper up a line without moving the print head back to the beginning of the line. So, on those devices, you needed two control characters to get the print head back to the start of the next line: a carriage return and a line feed. Because this was mechanical, it took time, so you had to pause for long enough before sending more characters to the terminal after sending the CR and LF characters. One use for CR without LF was to do 'bold' by overstriking the characters on the line. You'd write the line out once, then use CR to start over and print twice over the characters that needed to be bold. You could also, of course, type X's over stuff that you wanted partially hidden, or create very dense ASCII art pictures with judicious overstriking.
On Unix, all the logic for this stuff was hidden in a terminal driver. You could use the stty command and the underlying functions (in those days, ioctl() calls; they were sanitized into the termios interface by POSIX.1 in 1988) to tweak all sorts of ways that the terminal behaved.
Eventually, you got 'glass terminals' where the speeds were greater and and there were new idiosyncrasies to deal with - Hazeltine glitches and so on and so forth. These got enshrined in the termcap and later terminfo libraries, and then further encapsulated behind the curses library.
However, some other (non-Unix) systems did not hide things as well, and you had to deal with CRLF in your text files - and no, this is not just Windows and DOS that were in the 'CRLF' camp.
Anyway, on some systems, the C library has to deal with text files that contain CRLF line endings and presents those to you as if there were only a newline at the end of the line. However, if you choose to treat the text file as a binary file, you will see the CR characters as well as the LF.
Systems like the old Mac OS (version 9 or earlier) used just CR (aka \r) for the line ending. Systems like DOS and Windows (and, I believe, many of the DEC systems such as VMS and RSTS) used CRLF for the line ending. Many of the Internet standards (such as mail) mandate CRLF line endings. And Unix has always used just LF (aka NL or newline, hence \n) for its line endings. And most people, most of the time, manage to ignore CR.
Your code is rather funky in looking for \r. On a system compliant with the C standard, you won't see the CR unless the file is opened in binary mode; the CRLF or CR will be mapped to NL by the C runtime library.