When doing a git diff it says "No newline at end of file".

What's the significance of the message and what's it trying to tell us?

It indicates that you do not have a newline (usually \n, aka LF or CRLF) at the end of file.

That is, simply speaking, the last byte (or bytes if you're on Windows) in the file is not a newline.

The message is displayed because otherwise there is no way to tell the difference between a file where there is a newline at the end and one where is not. Diff has to output a newline anyway, or the result would be harder to read or process automatically.

Note that it is a good style to always put the newline as a last character, in text files, if it is allowed by the file format. Furthermore, for example, for C and C++ header files it is required by the language standard.