Different Operating Systems (OS X, *nix, Windows) have different 'symbols' for what constitutes the end of a line. There are two such symbols: the NewLine symbole (often call LF, and represented in Java Strings as "\n") and the CarriageReturn (CR, or "\r"). Some OSes (for example Windows) use both symbols in the order of CR LF ("\r\n") while others use just one symbol or the other.
What that sentence in the JLS is saying that it allows any of the 3 end-of-line conventions (CR, LF, or CR LF) to designate the end of a line of code, and that the line numbers will be consistent regardless of the convention used. For example, even though Windows uses two symbols for the end-of-line, the number of lines of code will still be counted as just one, not two.
This is important because it allows error messages to be reported the same way across platforms. For example if you take code with a compile error in it and copy it from Windows to Linux you would get the same reported line of code in the error message. So you know where the error occurs regardless of OS.
There are actually six line terminators, which are listed in the Pattern class. You will encounter LF and CR‑LF frequently. CR alone was used by old Macs, but newer Macs use LF, as used by Unix and Linux. Windows® uses CR‑LF.